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Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621
BuyFind

Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621

Solutions

Chapter
Section
Chapter 7.1, Problem 47E
Textbook Problem

(a) Use the reduction formula in Example 6 to show that

sin 2 x   d x = x 2 sin 2 x 4 + C

(b) Use part(a) and the reduction formula to evaluate sin 4 x   d x .

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Chapter 7 Solutions

Calculus (MindTap Course List)
Show all chapter solutions
Ch. 7.1 - Evaluate the integral. t4lntdtCh. 7.1 - Evaluate the integral. tan12ydyCh. 7.1 - Evaluate the integral. tcsc2tdtCh. 7.1 - Evaluate the integral. xcoshaxdxCh. 7.1 - Evaluate the integral. (lnx)2dxCh. 7.1 - Evaluate the integral. z10zdzCh. 7.1 - Evaluate the integral. e2sin3dCh. 7.1 - Evaluate the integral. ecos2dCh. 7.1 - Evaluate the integral. z3ezdzCh. 7.1 - Evaluate the integral. xtan2xdxCh. 7.1 - Evaluate the integral. xe2x(1+2x)2dxCh. 7.1 - Evaluate the integral. (arcsinx)2dxCh. 7.1 - Evaluate the integral. 01/2xcosxxdxCh. 7.1 - Evaluate the integral. 01(x2+1)exdxCh. 7.1 - Evaluate the integral. 02ysinhydyCh. 7.1 - Evaluate the integral. 12w2lnwdwCh. 7.1 - Evaluate the integral. 15lnRR2dRCh. 7.1 - Evaluate the integral. 02t2sin2tdtCh. 7.1 - Evaluate the integral. 0xsinxcosxdxCh. 7.1 - Evaluate the integral. 13arctan(1/x)dxCh. 7.1 - Evaluate the integral. 15MeMdMCh. 7.1 - Evaluate the integral. 12(lnx)2x3dxCh. 7.1 - Evaluate the integral. 0/3sinxln(cosx)dxCh. 7.1 - Evaluate the integral. 01r34+r2drCh. 7.1 - Evaluate the integral. 12x4(lnx)2dxCh. 7.1 - Evaluate the integral. 0tessin(ts)dsCh. 7.1 - First make a substitution and then use integration...Ch. 7.1 - First make a substitution and then use integration...Ch. 7.1 - First make a substitution and then use integration...Ch. 7.1 - First make a substitution and then use integration...Ch. 7.1 - First make a substitution and then use integration...Ch. 7.1 - First make a substitution and then use integration...Ch. 7.1 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.1 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.1 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.1 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.1 - a Use the reduction formula in Example 6 to show...Ch. 7.1 - a Prove the reduction formula...Ch. 7.1 - a Use the reduction formula in Example 6 to show...Ch. 7.1 - Prove that, for even powers of sine,...Ch. 7.1 - Use integration by parts to prove the reduction...Ch. 7.1 - Use integration by parts to prove the reduction...Ch. 7.1 - Use integration by parts to prove the reduction...Ch. 7.1 - Use integration by parts to prove the reduction...Ch. 7.1 - Use Exercise 51 to find (lnx)3dx.Ch. 7.1 - Use Exercise 52 to find x4exdx.Ch. 7.1 - Find the area of the region bounded by the given...Ch. 7.1 - Find the area of the region bounded by the given...Ch. 7.1 - Use a graph to find approximate x-coordinates of...Ch. 7.1 - Use a graph to find approximate x-coordinates of...Ch. 7.1 - Use the method of cylindrical shells to find the...Ch. 7.1 - Use the method of cylindrical shells to find the...Ch. 7.1 - Use the method of cylindrical shells to find the...Ch. 7.1 - Use the method of cylindrical shells to find the...Ch. 7.1 - Calculate the volume generated by rotating the...Ch. 7.1 - Calculate the average value of f(x)=xsec2x on the...Ch. 7.1 - The Fresnel function S(x)=0xsin(12t2)dt was...Ch. 7.1 - A rocket accelerates by burning its onboard fuel,...Ch. 7.1 - A particle that moves along a straight line has...Ch. 7.1 - If f(0)=g(0)=0 and f and g are continuous, show...Ch. 7.1 - Suppose that f(1)=2,f(4)=7,f(1)=5,f(4)=3, and f is...Ch. 7.1 - a Use integration by parts to show that...Ch. 7.1 - We arrived at Formula 5.3.2, V=ab2xf(x)dx, by...Ch. 7.1 - Let In=0/2sinnxdx. a Show that I2n+2I2n+1I2n. b...Ch. 7.2 - Evaluate the integral. sin2xcos3xdxCh. 7.2 - Evaluate the integral. sin3cos4dCh. 7.2 - Evaluate the integral. 0/2sin7cos5dCh. 7.2 - Evaluate the integral. 0/2sin5xdxCh. 7.2 - Evaluate the integral. sin5(2t)cos2(2t)dtCh. 7.2 - Evaluate the integral. tcos5(t2)dtCh. 7.2 - Evaluate the integral. 0/2cos2dCh. 7.2 - Evaluate the integral. 02sin2(13)dCh. 7.2 - Evaluate the integral. 0cos4(2t)dtCh. 7.2 - Evaluate the integral. 0sin2tcos4tdtCh. 7.2 - Evaluate the integral. 0/2sin2xcos2xdxCh. 7.2 - Evaluate the integral. 0/2(2sin)2dCh. 7.2 - Evaluate the integral. cossin3dCh. 7.2 - Evaluate the integral. sin2(1/t)t2dtCh. 7.2 - Evaluate the integral. cotxcos2xdxCh. 7.2 - Evaluate the integral. tan2xcos3xdxCh. 7.2 - Evaluate the integral. sin2xsin2xdxCh. 7.2 - Evaluate the integral. sinxcos(12x)dxCh. 7.2 - Evaluate the integral. tsin2tdtCh. 7.2 - Evaluate the integral. xsin3xdxCh. 7.2 - Evaluate the integral. tanxsec3xdxCh. 7.2 - Evaluate the integral. tan2sec4dCh. 7.2 - Evaluate the integral. tan2xdxCh. 7.2 - Evaluate the integral. (tan2x+tan4x)dxCh. 7.2 - Evaluate the integral. tan4xsec6xdxCh. 7.2 - Evaluate the integral. 0/4sec6tan6dCh. 7.2 - Evaluate the integral. tan3xsecxdxCh. 7.2 - Evaluate the integral. tan5xsec3xdxCh. 7.2 - Evaluate the integral. tan3xsec6xdxCh. 7.2 - Evaluate the integral. 0/4tan4tdtCh. 7.2 - Evaluate the integral. tan5xdxCh. 7.2 - Evaluate the integral. tan2xsecxdxCh. 7.2 - Evaluate the integral. xsecxtanxdxCh. 7.2 - Evaluate the integral. sincos3dCh. 7.2 - Evaluate the integral. /6/2cot2xdxCh. 7.2 - Evaluate the integral. /4/2cot3xdxCh. 7.2 - Evaluate the integral. /4/2cot5csc3dCh. 7.2 - Evaluate the integral. /4/2csc4cot4dCh. 7.2 - Evaluate the integral. cscxdxCh. 7.2 - Evaluate the integral. /6/3csc3xdxCh. 7.2 - Evaluate the integral. sin8xcos5xdxCh. 7.2 - Evaluate the integral. sin2sin6dCh. 7.2 - Evaluate the integral. 0/2cos5tcos10tdtCh. 7.2 - Evaluate the integral. sinxsec5xdxCh. 7.2 - Evaluate the integral. 0/61+cos2xdxCh. 7.2 - Evaluate the integral. 0/41cos4dCh. 7.2 - Evaluate the integral. 1tan2xsec2xdxCh. 7.2 - Evaluate the integral. dxcosx1Ch. 7.2 - Evaluate the integral. xtan2xdxCh. 7.2 - If 0/4tan6xsecxdx=I, express the value of...Ch. 7.2 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.2 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.2 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.2 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.2 - Find the average value of the function...Ch. 7.2 - Evaluate sinxcosxdx by four methods: a the...Ch. 7.2 - Find the area of the region bounded by the given...Ch. 7.2 - Find the area of the region bounded by the given...Ch. 7.2 - Use a graph of the integrated to guess the value...Ch. 7.2 - Use a graph of the integrated to guess the value...Ch. 7.2 - Find the volume obtained by rotating the region...Ch. 7.2 - Find the volume obtained by rotating the region...Ch. 7.2 - Find the volume obtained by rotating the region...Ch. 7.2 - Find the volume obtained by rotating the region...Ch. 7.2 - A particle moves on a straight line with velocity...Ch. 7.2 - Household electricity is supplied in the form of...Ch. 7.2 - Prove the formula, where m and n are positive...Ch. 7.2 - Prove the formula, where m and n are positive...Ch. 7.2 - Prove the formula, where m and n are positive...Ch. 7.2 - A finite Fourier series is given by the sum...Ch. 7.3 - Evaluate the integral using the indicated...Ch. 7.3 - Evaluate the integral using the indicated...Ch. 7.3 - Evaluate the integral using the indicated...Ch. 7.3 - Evaluate the integral. x29x2dxCh. 7.3 - Evaluate the integral. x21x4dxCh. 7.3 - Evaluate the integral. 03x36x2dxCh. 7.3 - Evaluate the integral. 0adx(a2+x2)3/2a0Ch. 7.3 - Evaluate the integral. dtt2t216Ch. 7.3 - Evaluate the integral. 23dx(x21)3/2Ch. 7.3 - Evaluate the integral. 02/349x2dxCh. 7.3 - Evaluate the integral. 01/2x14x2dxCh. 7.3 - Evaluate the integral. 02dt4+t2Ch. 7.3 - Evaluate the integral. x29x3dxCh. 7.3 - Evaluate the integral. 01dx(x2+1)2Ch. 7.3 - Evaluate the integral. 0ax2a2x2dxCh. 7.3 - Evaluate the integral. 2/32/3dxx59x21Ch. 7.3 - Evaluate the integral. xx27dxCh. 7.3 - Evaluate the integral. dx[(ax)2b2]3/2Ch. 7.3 - Evaluate the integral. 1+x2xdxCh. 7.3 - Evaluate the integral. x1+x2dxCh. 7.3 - Evaluate the integral. 00.6x2925x2dxCh. 7.3 - Evaluate the integral. 01x2+1dxCh. 7.3 - Evaluate the integral. dxx2+2x+5Ch. 7.3 - Evaluate the integral. 01xx2dxCh. 7.3 - Evaluate the integral. x23+2xx2dxCh. 7.3 - Evaluate the integral. x2(3+4x4x2)3/2dxCh. 7.3 - Evaluate the integral. x2+2xdxCh. 7.3 - Evaluate the integral. x2+1(x22x+2)2dxCh. 7.3 - Evaluate the integral. x1x4dxCh. 7.3 - Evaluate the integral. 0/2cost1+sin2tdtCh. 7.3 - a Use trigonometric substitution to show that...Ch. 7.3 - Evaluate x2(x2+a2)3/2dx a by trigonometric...Ch. 7.3 - Find the average value of f(x)=x21/x,1x7.Ch. 7.3 - Find the area of the region bounded by the...Ch. 7.3 - Prove the formula A=12r2 for the area of a sector...Ch. 7.3 - Evaluate the integral dxx4x22 Graph the integrand...Ch. 7.3 - Find the volume of the solid obtained by rotating...Ch. 7.3 - Find the volume of the solid obtained by rotating...Ch. 7.3 - a Use trigonometric substitution to verify that...Ch. 7.3 - The parabola y=12x2 divides the disk x2+y28 into...Ch. 7.3 - A torus is generated by rotating the circle...Ch. 7.3 - A charged rod of length L produces an electric...Ch. 7.3 - Find the area of the crescent-shaped region called...Ch. 7.3 - A water storage tank has the shape of a cylinder...Ch. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Evaluate the integral. x4x1dxCh. 7.4 - Evaluate the integral. 3t2t+1dtCh. 7.4 - Evaluate the integral. 5x+1(2x+1)(x1)dxCh. 7.4 - Evaluate the integral. y(y+4)(2y1)dyCh. 7.4 - Evaluate the integral. 0122x2+3x+1dxCh. 7.4 - Evaluate the integral. 01x4x25x+6dxCh. 7.4 - Evaluate the integral. axx2bxdxCh. 7.4 - Evaluate the integral. 1(x+a)(x+b)dxCh. 7.4 - Evaluate the integral. 10x34x+1x23x+2dxCh. 7.4 - Evaluate the integral. 12x2+4x2+x1x3+x2dxCh. 7.4 - Evaluate the integral. 124y27y12y(y+2)(y3)dyCh. 7.4 - Evaluate the integral. 123x2+6x+2x2+3x+2dxCh. 7.4 - Evaluate the integral. 01x2+x+1(x+1)2(x+2)dxCh. 7.4 - Evaluate the integral. 23x(35x)(3x1)(x1)2dxCh. 7.4 - Evaluate the integral. dt(t21)2Ch. 7.4 - Evaluate the integral. x4+9x2+x+2x2+9dxCh. 7.4 - Evaluate the integral. 10(x1)(x2+9)dxCh. 7.4 - Evaluate the integral. x2x+6x3+3xdxCh. 7.4 - Evaluate the integral. 4xx3+x2+x+1dxCh. 7.4 - Evaluate the integral. x2+x+1(x2+1)2dxCh. 7.4 - Evaluate the integral. x3+4x+3x4+5x2+4dxCh. 7.4 - Evaluate the integral. x3+6x2x4+6x2dxCh. 7.4 - Evaluate the integral. x+4x2+2x+5dxCh. 7.4 - Evaluate the integral. x32x2+2x5x4+4x2+3dxCh. 7.4 - Evaluate the integral. 1x31dxCh. 7.4 - Evaluate the integral. 01xx2+4x+13dxCh. 7.4 - Evaluate the integral. 01x3+2xx4+4x2+3dxCh. 7.4 - Evaluate the integral. x5+x1x3+1dxCh. 7.4 - Evaluate the integral. 5x4+7x2+x+2x(x2+1)2dxCh. 7.4 - Evaluate the integral. x4+3x2+1x5+5x3+5xdxCh. 7.4 - Evaluate the integral. x23x+7(x24x+6)2dxCh. 7.4 - Evaluate the integral. x3+2x2+3x2(x2+2x+2)2dxCh. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Use integration by parts, together with the...Ch. 7.4 - Use integration by parts, together with the...Ch. 7.4 - Use a graph of f(x)=1/(x22x3) to decide whether...Ch. 7.4 - Evaluate 1x2+kdx by considering several cases for...Ch. 7.4 - Evaluate the integral by completing the square and...Ch. 7.4 - Evaluate the integral by completing the square and...Ch. 7.4 - The German mathematician Karl Weierstrass 18151897...Ch. 7.4 - Use the substitution in Exercise 59 to transform...Ch. 7.4 - Use the substitution in Exercise 59 to transform...Ch. 7.4 - Use the substitution in Exercise 59 to transform...Ch. 7.4 - Use the substitution in Exercise 59 to transform...Ch. 7.4 - Find the area of the region under the given curve...Ch. 7.4 - Find the area of the region under the given curve...Ch. 7.4 - Find the volume of the resulting solid if the...Ch. 7.4 - One method of slowing the growth of an insect...Ch. 7.4 - Factor x4+1 as a difference of squares by first...Ch. 7.4 - a Use a computer algebra system to find the...Ch. 7.4 - a Find the partial fraction decomposition of the...Ch. 7.4 - The rational number 227 has been used as an...Ch. 7.4 - a Use integration by parts to show that, for any...Ch. 7.4 - Suppose that F, G, and Q are polynomials and...Ch. 7.4 - If f is a quadratic function such that f(0)=1 and...Ch. 7.4 - If a0 and n is a positive integer, find the...Ch. 7.5 - Evaluate the integral. cosx1sinxdxCh. 7.5 - Evaluate the integral. 01(3x+1)2dxCh. 7.5 - Evaluate the integral. 14ylnydyCh. 7.5 - Evaluate the integral. sin3xcosxdxCh. 7.5 - Evaluate the integral. tt4+2dtCh. 7.5 - Evaluate the integral. 01x(2x+1)3dxCh. 7.5 - Evaluate the integral. 11earctany1+y2dyCh. 7.5 - Evaluate the integral. tsintcostdtCh. 7.5 - Evaluate the integral. 24x+2x2+3x4dxCh. 7.5 - Evaluate the integral. cos(1/x)x3dxCh. 7.5 - Evaluate the integral. 1x3x21dxCh. 7.5 - Evaluate the integral. 2x3x3+3xdxCh. 7.5 - Evaluate the integral. sin5tcos4tdtCh. 7.5 - Evaluate the integral. ln(1+x2)dxCh. 7.5 - Evaluate the integral. xsecxtanxdxCh. 7.5 - Evaluate the integral. 02/2x21x2dxCh. 7.5 - Evaluate the integral. 0tcos2tdtCh. 7.5 - Evaluate the integral. 14ettdtCh. 7.5 - Evaluate the integral. ex+exdxCh. 7.5 - Evaluate the integral. e2dxCh. 7.5 - 7.5 EXERCISES Evaluate the integral. arctanxdxCh. 7.5 - Evaluate the integral. lnxx1+(lnx)2dxCh. 7.5 - Evaluate the integral. 01(1+x)8dxCh. 7.5 - Evaluate the integral. (1+tanx)2secxdxCh. 7.5 - Evaluate the integral. 011+12t1+3tdtCh. 7.5 - Evaluate the integral. 013x2+1x3+x2+x+1dxCh. 7.5 - Evaluate the integral. dx1+exCh. 7.5 - 7.5 EXERCISES Evaluate the integral. sinatdtCh. 7.5 - Evaluate the integral. ln(x+x21)dxCh. 7.5 - Evaluate the integral. 12|ex1|dxCh. 7.5 - Evaluate the integral. 1+x1xdxCh. 7.5 - Evaluate the integral. 13e3/xx2dxCh. 7.5 - Evaluate the integral. 32xx2dxCh. 7.5 - 7.5 EXERCISES Evaluate the integral....Ch. 7.5 - Evaluate the integral. /2/2x1+cos2xdxCh. 7.5 - Evaluate the integral. 1+sinx1+cosxdxCh. 7.5 - Evaluate the integral. 0/4tan3sec2dCh. 7.5 - Evaluate the integral. /6/3sincotsecdCh. 7.5 - Evaluate the integral. sectansec2secdCh. 7.5 - 7.5 EXERCISES Evaluate the integral. 0sin6xcos3xdxCh. 7.5 - Evaluate the integral. tan2dCh. 7.5 - Evaluate the integral. tan1xx2dxCh. 7.5 - Evaluate the integral. x1+x3dxCh. 7.5 - Evaluate the integral. 1+exdxCh. 7.5 - Evaluate the integral. x5ex3dxCh. 7.5 - Evaluate the integral. (x1)exx2dxCh. 7.5 - 7.5 EXERCISES Evaluate the integral. x3(x1)4dxCh. 7.5 - Evaluate the integral. 01x21x2dxCh. 7.5 - Evaluate the integral. 1x4x+1dxCh. 7.5 - Evaluate the integral. 1x24x+1dxCh. 7.5 - Evaluate the integral. 1x4x2+1dxCh. 7.5 - Evaluate the integral. dxx(x4+1)Ch. 7.5 - 7.5 EXERCISES Evaluate the integral. x2sinhmxdxCh. 7.5 - Evaluate the integral. (x+sinx)2dxCh. 7.5 - Evaluate the integral. dxx+xxCh. 7.5 - Evaluate the integral. dxx+xxCh. 7.5 - Evaluate the integral. xx+c3dxCh. 7.5 - Evaluate the integral. xlnxx21dxCh. 7.5 - Evaluate the integral. dxx416Ch. 7.5 - Evaluate the integral. dxx24x21Ch. 7.5 - Evaluate the integral. d1+cosCh. 7.5 - Evaluate the integral. d1+cos2Ch. 7.5 - Evaluate the integral. xexdxCh. 7.5 - Evaluate the integral. 1x+1dxCh. 7.5 - Evaluate the integral. sin2x1+cos4xdxCh. 7.5 - Evaluate the integral. /4/3ln(tanx)sinxcosxdxCh. 7.5 - Evaluate the integral. 1x+1+xdxCh. 7.5 - Evaluate the integral. x2x6+3x3+2dxCh. 7.5 - Evaluate the integral. 131+x2x2dxCh. 7.5 - Evaluate the integral. 11+2exexdxCh. 7.5 - Evaluate the integral. e2x1+exdxCh. 7.5 - 7.5 EXERCISES Evaluate the integral. ln(x+1)x2dxCh. 7.5 - Evaluate the integral. x+arcsinx1x2dxCh. 7.5 - Evaluate the integral. 4x+10x2xdxCh. 7.5 - Evaluate the integral. dxxlnxxCh. 7.5 - Evaluate the integral. x2x2+1dxCh. 7.5 - Evaluate the integral. xex1+exdxCh. 7.5 - Evaluate the integral. 1+sinx1sinxdxCh. 7.5 - 7.5 EXERCISES Evaluate the integral. xsin2xcosxdxCh. 7.5 - Evaluate the integral. secxcos2xsinx+secxdxCh. 7.5 - Evaluate the integral. 1sinxdxCh. 7.5 - Evaluate the integral. sinxcosxsin4x+cos4xdxCh. 7.5 - The functions y=ex2 and y=x2ex2 dont have...Ch. 7.5 - We know that F(x)=0xeetdt is a continuous function...Ch. 7.6 - Use the indicated entry in the Table of Integrals...Ch. 7.6 - Use the indicated entry in the Table of Integrals...Ch. 7.6 - Use the indicated entry in the Table of Integrals...Ch. 7.6 - Use the indicated entry in the Table of Integrals...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - Use the Table of Integrals on Reference Pages 610...Ch. 7.6 - The region under the curve y=sin2x from 0 to is...Ch. 7.6 - Find the volume of the solid obtained when the...Ch. 7.6 - Verify Formula 53 in the Table of Integrals a by...Ch. 7.6 - Verify Formula 31 a by differentiation and b by...Ch. 7.6 - Use a computer algebra system to evaluate the...Ch. 7.6 - Use a computer algebra system to evaluate the...Ch. 7.6 - Use a computer algebra system to evaluate the...Ch. 7.6 - Use a computer algebra system to evaluate the...Ch. 7.6 - 3744 Use a computer algebra system to evaluate the...Ch. 7.6 - Use a computer algebra system to evaluate the...Ch. 7.6 - Use a computer algebra system to evaluate the...Ch. 7.6 - Use a computer algebra system to evaluate the...Ch. 7.6 - a Use the table of integrals to evaluate...Ch. 7.6 - Computer algebra systems sometimes need a helping...Ch. 7.7 - Let I=04f(x)dx, where f is the function whose...Ch. 7.7 - The left, right, Trapezoidal, and Midpoint Rule...Ch. 7.7 - Estimate 01cos(x2)dx using a the Trapezoidal Rule...Ch. 7.7 - Draw the graph of f(x)=sin(12x2) in the viewing...Ch. 7.7 - Use a the Midpoint Rule and b Simpsons Rule to...Ch. 7.7 - Use a the Midpoint Rule and b Simpsons Rule to...Ch. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.7 - a Find the approximations T8 and M8 for the...Ch. 7.7 - a Find the approximations T10 and M10 for...Ch. 7.7 - a Find the approximations T10, M10, and S10 for...Ch. 7.7 - How large should n be to guarantee that the...Ch. 7.7 - The trouble with the error estimates is that it is...Ch. 7.7 - Repeat Exercise 23 for the integral 114x3dx. The...Ch. 7.7 - Find the approximations Ln, Rn, Tn and Mn for n=5,...Ch. 7.7 - Find the approximations Ln, Rn, Tn and Mn for n=5,...Ch. 7.7 - Find the approximations Tn, Mn, and Sn for n=6 and...Ch. 7.7 - Find the approximations Tn, Mn, and Sn for n=6 and...Ch. 7.7 - Estimate the area under the graph in the figure by...Ch. 7.7 - The widths in meters of a kidney-shaped swimming...Ch. 7.7 - a Use the Midpoint Rule and the given data to...Ch. 7.7 - a A table of values of a function g is given. Use...Ch. 7.7 - A graph of the temperature in Boston on August 11,...Ch. 7.7 - A radar gun was used to record the speed of a...Ch. 7.7 - The graph of the acceleration at of a car measured...Ch. 7.7 - Water leaked from a tank at a rate of rt liters...Ch. 7.7 - The table supplied by San Diego Gas and Electric...Ch. 7.7 - Shown is the graph of traffic on an Internet...Ch. 7.7 - Use Simpsons Rule with n=8 to estimate the volume...Ch. 7.7 - The table shows values of a force function fx,...Ch. 7.7 - The region bounded by the curve y=1/(1+ex), the x-...Ch. 7.7 - The figure shows a pendulum with length L that...Ch. 7.7 - The intensity of light with wavelength traveling...Ch. 7.7 - Use the Trapezoidal Rule with n=10 to approximate...Ch. 7.7 - Sketch the graph of a continuous function on 0, 2...Ch. 7.7 - Sketch the graph of a continuous function on 0, 2...Ch. 7.7 - If f is a positive function and f(x)0 for axb,...Ch. 7.7 - Show that if f is a polynomial of degree 3 or...Ch. 7.7 - Show that 12(Tn+Mn)=T2n.Ch. 7.7 - Show that 13Tn+23Mn=S2n.Ch. 7.8 - Explain why each of the following integrals is...Ch. 7.8 - Which of the following integrals are improper?...Ch. 7.8 - Find the area under the curve y=1/x3 from x=1 to...Ch. 7.8 - a Graph the functions f(x)=1/x1.1 and g(x)=1/x0.9...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Sketch the region and find its area if the area is...Ch. 7.8 - Sketch the region and find its area if the area is...Ch. 7.8 - Sketch the region and find its area if the area is...Ch. 7.8 - Sketch the region and find its area if the area is...Ch. 7.8 - Sketch the region and find its area if the area is...Ch. 7.8 - Sketch the region and find its area if the area is...Ch. 7.8 - a If g(x)=(sin2x)/x2, use your calculator or...Ch. 7.8 - a If g(x)=1/(x1), use your calculator or computer...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - The integral 01x(1+x)dx is improper for two...Ch. 7.8 - Evaluate 21xx24dx by the same method as in...Ch. 7.8 - Find the values of p for which the integral...Ch. 7.8 - Find the values of p for which the integral...Ch. 7.8 - Find the values of p for which the integral...Ch. 7.8 - a Evaluate the integral 0xnexdx for n = 0, 1, 2,...Ch. 7.8 - a Show that xdx is divergent. b Show that...Ch. 7.8 - The average speed of molecules in an ideal gas is...Ch. 7.8 - We know from Example 1 that the region...Ch. 7.8 - Use the information and data in Exercise 5.4.33 to...Ch. 7.8 - Find the escape velocity v0 that is needed to...Ch. 7.8 - Astronomers use a technique called stellar...Ch. 7.8 - A manufacturer of lightbulbs wants to produce...Ch. 7.8 - As we saw in Section 6.5, a radioactive substance...Ch. 7.8 - In a study of the spread of illicit drug use from...Ch. 7.8 - Dialysis treatment removes urea and other waste...Ch. 7.8 - Determine how large the number a has to be so that...Ch. 7.8 - Estimate the numerical value of 0ex2dx by writing...Ch. 7.8 - If f(t) is continuous for t0, the Laplace...Ch. 7.8 - Show that if 0f(t)Meat for t0, where M and a are...Ch. 7.8 - Suppose that 0f(t)Meat and 0f(t)Keat for t0, where...Ch. 7.8 - If f(x)dx is convergent and a and b are real...Ch. 7.8 - Show that 0x2ex2dx=120ex2dx.Ch. 7.8 - Show that 0ex2dx=01lnydyby interpreting the...Ch. 7.8 - Find the value of the constant C for which the...Ch. 7.8 - Find the value of the constant C for which the...Ch. 7.8 - Suppose is continuous on [0,) and limxf(x)=1. Is...Ch. 7.8 - Show that if a1 and ba+1, then the following...Ch. 7.R - State the rule for integration by parts. In...Ch. 7.R - How do you evaluate sinmxcosnxdx if m is odd? What...Ch. 7.R - If the expression a2x2 occurs in an integral, what...Ch. 7.R - What is the form of the partial fraction...Ch. 7.R - State the rules for approximating the definite...Ch. 7.R - Define the following improper integrals. a af(x)dx...Ch. 7.R - Define the improper integral abf(x)dx for each of...Ch. 7.R - State the Comparison Theorem for improper...Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Determine whether the statement is true or false....Ch. 7.R - Evaluate the integral. 12(x+1)2xdxCh. 7.R - Evaluate the integral. 12x(x+1)2dxCh. 7.R - Evaluate the integral. esinxsecxdxCh. 7.R - Evaluate the integral. 0/6tsin2tdtCh. 7.R - Evaluate the integral. dt2t2+3t+1Ch. 7.R - Evaluate the integral. 12x5lnxdxCh. 7.R - Evaluate the integral. 0/2sin3cos2dCh. 7.R - Evaluate the integral. dxex1Ch. 7.R - Evaluate the integral. sin(lnt)tdtCh. 7.R - Evaluate the integral. 01arctanx1+x2dxCh. 7.R - Evaluate the integral. 12x21xdxCh. 7.R - Evaluate the integral. e2x1+e4xdxCh. 7.R - Evaluate the integral. ex3dxCh. 7.R - Evaluate the integral. x2+2x+2dxCh. 7.R - Evaluate the integral. x1x2+2xdxCh. 7.R - Evaluate the integral. sec6tan2dCh. 7.R - Evaluate the integral. xcoshxdxCh. 7.R - Evaluate the integral. x2+8x3x3+3x2dxCh. 7.R - Evaluate the integral. x+19x2+6x+5dxCh. 7.R - Evaluate the integral. tan5sec3dCh. 7.R - Evaluate the integral. dxx24xCh. 7.R - Evaluate the integral. costdtCh. 7.R - Evaluate the integral. dxxx2+1Ch. 7.R - Evaluate the integral. excosxdxCh. 7.R - Evaluate the integral. 3x3x2+6x4(x2+1)(x2+2)dxCh. 7.R - Evaluate the integral. xsinxcosxdxCh. 7.R - Evaluate the integral. 0/2cos3xsin2xdxCh. 7.R - Evaluate the integral. x3+1x31dxCh. 7.R - Evaluate the integral. 33x1+|x|dxCh. 7.R - Evaluate the integral. dxex1e2xCh. 7.R - 140 Evaluate the integral. 0In10exex1ex+8dxCh. 7.R - Evaluate the integral. 0/4xsinxcos3xdxCh. 7.R - Evaluate the integral. x2(4x2)3/2dxCh. 7.R - Evaluate the integral. (arcsinx)2dxCh. 7.R - Evaluate the integral. 1x+x3/2dxCh. 7.R - Evaluate the integral. 1tan1+tandCh. 7.R - Evaluate the integral. (cosx+sinx)2cos2xdxCh. 7.R - 140 Evaluate the integral. 2xxdxCh. 7.R - Evaluate the integral. 01/2xe2x(1+2x)2dxCh. 7.R - Evaluate the integral. /4/3tansin2dCh. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the integral or show that it is...Ch. 7.R - Evaluate the indefinite integral. Illustrate and...Ch. 7.R - Evaluate the indefinite integral. Illustrate and...Ch. 7.R - Graph the function f(x)=cos2xsin3x and use the...Ch. 7.R - a How would you evaluate x5e2xdx by hand? Dont...Ch. 7.R - Use the Table of Integrals on the Reference Pages...Ch. 7.R - Use the Table of Integrals on the Reference Pages...Ch. 7.R - Use the Table of Integrals on the Reference Pages...Ch. 7.R - Use the Table of Integrals on the Reference Pages...Ch. 7.R - Verify Formula 33 in the Table of Integrals a by...Ch. 7.R - Verify Formula 62 in the Table of Integrals.Ch. 7.R - Is it possible to find a number n such that 0xndx...Ch. 7.R - For what values of a is 0eaxcosxdx convergent?...Ch. 7.R - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.R - Use a the Trapezoidal Rule, b the Midpoint Rule,...Ch. 7.R - Estimate the errors involved in Exercise 63, parts...Ch. 7.R - Use Simpsons Rule with n=60 to estimate the area...Ch. 7.R - The speedometer reading v on a car was observed at...Ch. 7.R - A population of honeybees increased at a rate of...Ch. 7.R - a If f(x)=sin(sinx), use a graph to find an upper...Ch. 7.R - Suppose you are asked to estimate the volume of a...Ch. 7.R - Use the Comparison Theorem to determine whether...Ch. 7.R - Find the area of the region bounded by the...Ch. 7.R - Find the area bounded by the curves y=cosx and...Ch. 7.R - Find the area of the region bounded by the curves...Ch. 7.R - The region under the curve y=cos2x,0x/2, is...Ch. 7.R - The region in Exercise 75 is rotated about the...Ch. 7.R - If f is continuous on [0,) and limxf(x)=0, show...Ch. 7.R - We can extend our definition of average value of a...Ch. 7.R - Use the substitution u=1/x to show that...Ch. 7.R - The magnitude of the repulsive force between two...Ch. 7.P - Three mathematics students have ordered a 14-inch...Ch. 7.P - Evaluate 1x7xdx The straightforward approach would...Ch. 7.P - Evaluate 01(1x731x37)dx.Ch. 7.P - The centers of two disks with radius 1 are one...Ch. 7.P - An ellipse is cut out of a circle with radius a....Ch. 7.P - A man initially standing at the point O walks...Ch. 7.P - A function f is defined by f(x)=0costcos(xt)dt0x2...Ch. 7.P - If n is a positive integer, prove that...Ch. 7.P - Show that 01(1x2)ndx=22n(n!)2(2n+1)! Hint: Start...Ch. 7.P - Suppose that f is a positive function such that f...Ch. 7.P - If 0ab, find limt0{01[bx+a(1x)]tdx}1/tCh. 7.P - Graph f(x)=sin(ex) and use the graph to estimate...Ch. 7.P - Evaluate 1(x41+x6)2dx.Ch. 7.P - Evaluate tanxdx.Ch. 7.P - The circle with radius 1 shown in the figure...Ch. 7.P - A rocket is fired straight up, burning fuel at the...

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