BuyFind

Single Variable Calculus

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781305266636
BuyFind

Single Variable Calculus

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781305266636

Solutions

Chapter
Section
Chapter 4, Problem 1RCC
Textbook Problem

(a) Write an expression for a Riemann sum of a function f on an interval [a, b]. Explain the meaning of the notation that you use.

(b) If f ( x ) 0 , what is the geometric interpretation of a Riemann sum? Illustrate with a diagram.

(c) If f(x) takes on both positive and negative values, what is the geometric interpretation of a Riemann sum? Illustrate with a diagram.

Expert Solution

(a)

To determine

To find: The expression for a Riemann sum of a function f.

Answer to Problem 1RCC

The expression for a Riemann sum of a function f is i=1nf(xi*)Δx.

Explanation of Solution

The Riemann sum of a function f is the method to find the total area underneath a curve.

The area under the curve dividedas n number of approximating rectangles. Hence the Riemann sum of a function f is the sum of the area of the all individual rectangles.

R=i=1nf(xi*)Δx

Here, xi* is a point in the i subinterval [xi1,xi] and Δx is the length of the sub intervals.

Thus, the expression for a Riemann sum of a function f is i=1nf(xi*)Δx.

Expert Solution

b)

To determine

To define: The geometric interpretation of a Riemann sum with diagram.

Explanation of Solution

Given information:

Consider the condition for the function f(x)0

Explanation:

The function f(x)0 represents that the function is in the first quadrant of the graph.

Sketch the curve f(x) in the first quadrant and then separate the area under the curve with n number approximating rectangles.

Show the curve as in Figure 1.

Single Variable Calculus, Chapter 4, Problem 1RCC , additional homework tip  1

Refer to Figure 1

The function f(x) is positive. Hence the sum of areas of rectangles underneath the curve is the Riemann sum.

Thus, the geometric interpretation of a Riemann sum of f(x)0 is defined.

Expert Solution

c)

To determine

To define: The geometric interpretation of a Riemann sum, if the function f(x) takes on both positive and negative values.

Explanation of Solution

Given information:

The function f(x) takes on both positive and negative values.

Explanation:

The function f(x) takes on both positive and negative values represents that the function is in the first and fourth quadrant of the graph.

Sketch the curve f(x) in the first and third quadrant and then divide the area under the curve and above the curve with n number approximating rectangles.

Show the curve as in Figure 2.

Single Variable Calculus, Chapter 4, Problem 1RCC , additional homework tip  2

Refer figure 2,

The Riemann sum is the difference of areas of approximating rectangles above and below the x-axis

Therefore, the geometric interpretation of a Riemann sum is defined, if f(x) has both positive and negative values.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Get Solutions

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Get Solutions

Chapter 4 Solutions

Single Variable Calculus
Show all chapter solutions
Ch. 4.1 - Some computer algebra systems have commands that...Ch. 4.1 - (a) If f(x)=x/(x+2), 1 x 4, use the commands...Ch. 4.1 - The speed of a runner increased steadily during...Ch. 4.1 - The table shows speedometer readings at 10-second...Ch. 4.1 - Oil leaked from a tank at a rate of r(t) liters...Ch. 4.1 - When we estimate distances from velocity data, it...Ch. 4.1 - The velocity graph of a braking car is shown. Use...Ch. 4.1 - The velocity graph of a car accelerating from rest...Ch. 4.1 - In someone infected with measles, the virus level...Ch. 4.1 - The table shows the number of people per day who...Ch. 4.1 - Use Definition 2 to find an expression for the...Ch. 4.1 - Use Definition 2 to find an expression for the...Ch. 4.1 - Use Definition 2 to find an expression for the...Ch. 4.1 - Determine a region whose area is equal to the...Ch. 4.1 - Determine a region whose area is equal to the...Ch. 4.1 - (a) Use Definition 2 to find an expression for the...Ch. 4.1 - Let A be the area under the graph of an increasing...Ch. 4.1 - If A is the area under the curve y = sin x from 0...Ch. 4.1 - (a) Express the area under the curve y = x5 from 0...Ch. 4.1 - (a) Express the area under the curve y = x4 + 5x2...Ch. 4.1 - Find the exact area under the cosine curve y = cos...Ch. 4.1 - (a) Let An be the area of a polygon with n equal...Ch. 4.2 - Evaluate the Riemann sum for f(x)=x1,6x4, with...Ch. 4.2 - If f(x)=cosx0x3/4 evaluate the Riemann sum with n...Ch. 4.2 - If f(x)=x24,0x3, find the Riemann sum with n = 6,...Ch. 4.2 - (a) Find the Riemann sum for f(x)=1/x,1x2, with...Ch. 4.2 - The graph of a function f is given. Estimate...Ch. 4.2 - The graph of g is shown. Estimate 24g(x)dx with...Ch. 4.2 - A table of values of an increasing function f is...Ch. 4.2 - The table gives the values of a function obtained...Ch. 4.2 - Use the Midpoint Rule with the given value of n to...Ch. 4.2 - Use the Midpoint Rule with the given value of n to...Ch. 4.2 - Use the Midpoint Rule with the given value of n to...Ch. 4.2 - Use the Midpoint Rule with the given value of n to...Ch. 4.2 - If you have a CAS that evaluates midpoint...Ch. 4.2 - With a programmable calculator or computer (see...Ch. 4.2 - Use a calculator or computer to make a table of...Ch. 4.2 - Use a calculator or computer to make a table of...Ch. 4.2 - Express the limit as a definite integral on the...Ch. 4.2 - Express the limit as a definite integral on the...Ch. 4.2 - Express the limit as a definite integral on the...Ch. 4.2 - Express the limit as a definite integral on the...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - (a) Find an approximation to the integral...Ch. 4.2 - Prove that abxdx=b2a22.Ch. 4.2 - Prove that abx2dx=b3a33.Ch. 4.2 - Express the integral as a limit of Riemann sums....Ch. 4.2 - Express the integral as a limit of Riemann sums....Ch. 4.2 - Express the integral as a limit of sums. Then...Ch. 4.2 - Express the integral as a limit of sums. Then...Ch. 4.2 - The graph of f is shown. Evaluate each integral by...Ch. 4.2 - The graph of g consists of two straight lines and...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate 111+x4dx.Ch. 4.2 - Give that 0sin4xdx=38, what is 0sin4d?Ch. 4.2 - In Example 4.1.2 we showed that 01x2dx=13. Use...Ch. 4.2 - Use the properties of integrals and the result of...Ch. 4.2 - Use the results of Exercises 27 and 28 and the...Ch. 4.2 - Use the result of Exercise 27 and the fact that...Ch. 4.2 - Write as a single integral in the form abf(x)dx...Ch. 4.2 - If 28f(x)dx=7.3 and 24f(x)dx=5.9, find 48f(x)dx.Ch. 4.2 - If 09f(x)dx=37 and 09g(x)dx=16, find...Ch. 4.2 - Find 05f(x)dx if f(x)={3forx3xforx3Ch. 4.2 - For the function f whose graph is shown, list the...Ch. 4.2 - If F(x)=2f(t)dt, where f is the function whose...Ch. 4.2 - Each of the regions A, B, and C bounded by the...Ch. 4.2 - Suppose f has absolute minimum value m and...Ch. 4.2 - Use the properties of integrals to verify the...Ch. 4.2 - Use the properties of integrals to verify the...Ch. 4.2 - Use the properties of integrals to verify the...Ch. 4.2 - Use the properties of integrals to verify the...Ch. 4.2 - Use Property 8 of integrals to estimate the value...Ch. 4.2 - Use Property 8 of integrals to estimate the value...Ch. 4.2 - Use Property 8 of integrals to estimate the value...Ch. 4.2 - Use Property 8 of integrals to estimate the value...Ch. 4.2 - Use Property 8 of integrals to estimate the value...Ch. 4.2 - Use Property 8 of integrals to estimate the value...Ch. 4.2 - Use properties of integrals, together with...Ch. 4.2 - Use properties of integrals, together with...Ch. 4.2 - Which of the integrals 12xdx,121/xdx and 12xdx has...Ch. 4.2 - Which of the integrals 00.5cos(x2)dx,00.5cosxdx is...Ch. 4.2 - Prove Property 3 of integrals.Ch. 4.2 - (a) If f is continuous on [a, b], show that...Ch. 4.2 - Let f(x) = 0 if x is any rational number and f(x)...Ch. 4.2 - Let f(0) = 0 and f(x) = 1/x if 0 x 1. Show that...Ch. 4.2 - Express the limit as a definite integral. 73....Ch. 4.2 - Express the limit as a definite integral. 74....Ch. 4.2 - Find12x2dx. Hint: Choose xi to be the geometric...Ch. 4.3 - Explain exactly what is meant by the statement...Ch. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Sketch the area represented by g(x). Then find...Ch. 4.3 - Sketch the area represented by g(x). Then find...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Evaluate the integral. 19. 13(x2+2x4)dxCh. 4.3 - Evaluate the integral. 20. 11x100dxCh. 4.3 - Evaluate the integral. 21. 02(45t334t2+25t)dtCh. 4.3 - Evaluate the integral. 22. 01(18v3+16v2)dvCh. 4.3 - Evaluate the integral. 23. 19xdxCh. 4.3 - Evaluate the integral. 24. 18x-2/3dxCh. 4.3 - Evaluate the integral. 25. /6sindCh. 4.3 - Evaluate the integral. 26. 55dxCh. 4.3 - Evaluate the integral. 27. 01(u+2)(u3)duCh. 4.3 - Evaluate the integral. 28. 04(4t)tdtCh. 4.3 - Evaluate the integral. 29. 142+x2xdxCh. 4.3 - Evaluate the integral. 30. 12(3u2)(u+1)duCh. 4.3 - Evaluate the integral. 31. /6/2csctcottdtCh. 4.3 - Evaluate the integral. 32. /4/3csc2dCh. 4.3 - Evaluate the integral. 33. 00(1+r)3drCh. 4.3 - Evaluate the integral. 34. 12s4+1s2dsCh. 4.3 - Evaluate the integral. 35. 12v5+3v6v4dvCh. 4.3 - Evaluate the integral. 36. 1183zdzCh. 4.3 - Evaluate the integral. 37....Ch. 4.3 - Evaluate the integral. 38....Ch. 4.3 - Sketch the region enclosed by the given curves and...Ch. 4.3 - Sketch the region enclosed by the given curves and...Ch. 4.3 - Sketch the region enclosed by the given curves and...Ch. 4.3 - Sketch the region enclosed by the given curves and...Ch. 4.3 - Use a graph to give a rough estimate of the area...Ch. 4.3 - Use a graph to give a rough estimate of the area...Ch. 4.3 - Use a graph to give a rough estimate of the area...Ch. 4.3 - Use a graph to give a rough estimate of the area...Ch. 4.3 - Evaluate the integral and interpret it as a...Ch. 4.3 - Evaluate the integral and interpret it as a...Ch. 4.3 - What is wrong with the equation? 49....Ch. 4.3 - What is wrong with the equation? 50....Ch. 4.3 - What is wrong with the equation? 51....Ch. 4.3 - What is wrong with the equation? 52....Ch. 4.3 - Find the derivative of the function. 53....Ch. 4.3 - Find the derivative of the function. 54....Ch. 4.3 - Find the derivative of the function. 55....Ch. 4.3 - Find the derivative of the function. 56....Ch. 4.3 - Let F(x)=xcosttdt. Find an equation of the tangent...Ch. 4.3 - If f(x)=0x(1t2)cos2tdt, on what interval is f...Ch. 4.3 - On what interval is the curve y=0xt2t2+t+2dt...Ch. 4.3 - Let F(x)=1xf(t)dt, where f is the function whose...Ch. 4.3 - If f(1) = 12, f is continuous, and 14f(x)dx=17,...Ch. 4.3 - If f(x)=0sinx1+t2dt and g(y)=3yf(x)dx, find g(/6).Ch. 4.3 - The Fresnel function S was defined in Example 3...Ch. 4.3 - The sine integral function Si(x)=0xsinttdt is...Ch. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Evaluate the limit by first recognizing the sum as...Ch. 4.3 - Evaluate the limit by first recognizing the sum as...Ch. 4.3 - Justify (3) for the case h 0.Ch. 4.3 - If f is continuous and g and h are differentiable...Ch. 4.3 - (a) Show that 11+x31+x3 for x 0. (b) Show that...Ch. 4.3 - (a) Show that cos(x2) cos x for 0 x 1. (b)...Ch. 4.3 - Show that 0510x2x4+x2+1dx0.1 by comparing the...Ch. 4.3 - Let f(x)={0ifx0xif0x12xif1x20ifx2 and...Ch. 4.3 - Find a function f and a number a such that...Ch. 4.3 - Suppose h is a function such that h(1) = 2, h(1) =...Ch. 4.3 - A manufacturing company owns a major piece of...Ch. 4.3 - A high-tech company purchases a new computing...Ch. 4.3 - Evaluate the integral. 79. 1912xdxCh. 4.3 - Evaluate the integral 80. 0110xdxCh. 4.3 - The following exercises are intended only for...Ch. 4.3 - Evaluate the integral 82. 014t2+1dtCh. 4.3 - Evaluate the integral 83. 11eu+1duCh. 4.3 - The following exercises are intended only for...Ch. 4.4 - Verify by differentiation that the formula is...Ch. 4.4 - Verify by differentiation that the formula is...Ch. 4.4 - Verify by differentiation that the formula is...Ch. 4.4 - Verify by differentiation that the formula is...Ch. 4.4 - Find the general indefinite integral. 5....Ch. 4.4 - Find the general indefinite integral. 6. x54dxCh. 4.4 - Find the general indefinite integral. 7....Ch. 4.4 - Find the general indefinite integral. 8....Ch. 4.4 - Find the general indefinite integral. 9....Ch. 4.4 - Find the general indefinite integral. 10....Ch. 4.4 - Find the general indefinite integral. 11. 1+x+xxdxCh. 4.4 - Find the general indefinite integral. 12....Ch. 4.4 - Find the general indefinite integral. 13....Ch. 4.4 - Find the general indefinite integral. 14....Ch. 4.4 - Find the general indefinite integral. 15....Ch. 4.4 - Find the general indefinite integral. 16....Ch. 4.4 - Find the general indefinite integral. Illustrate...Ch. 4.4 - Find the general indefinite integral. Illustrate...Ch. 4.4 - Evaluate the integral. 19. 23(x23)dxCh. 4.4 - Evaluate the integral. 20. 12(4x33x2+2x)dxCh. 4.4 - Evaluate the integral. 21. 20(12t4+14t3t)dtCh. 4.4 - Evaluate the integral. 22. 03(1+6w210w4)dwCh. 4.4 - Evaluate the integral. 23. 02(2x3)(4x2+1)dxCh. 4.4 - Evaluate the integral. 24. 11t(1t)2dtCh. 4.4 - Evaluate the integral. 25. 0(4sin3cos)dCh. 4.4 - Evaluate the integral. 26. 12(1x24x3)dxCh. 4.4 - Evaluate the integral. 27. 14(4+6uu)duCh. 4.4 - Evaluate the integral. 28. 12(21p2)2dpCh. 4.4 - Evaluate the integral. 29. 145xdxCh. 4.4 - Evaluate the integral. 30. 18(2w3w3)dwCh. 4.4 - Evaluate the integral. 31. 14t(1+t)dtCh. 4.4 - Evaluate the integral. 32. 0/4sectandCh. 4.4 - Evaluate the integral. 33. 0/41+cos2cos2dCh. 4.4 - Evaluate the integral. 34. 0/3sin+sintan2sec2dCh. 4.4 - Evaluate the integral. 35. 182+tt23dtCh. 4.4 - Evaluate the integral. 36. 064u(uu3)duCh. 4.4 - Evaluate the integral. 37. 01(x54+x45)dxCh. 4.4 - Evaluate the integral. 38. 01(1+x2)3dxCh. 4.4 - Evaluate the integral. 39. 25|x3|dxCh. 4.4 - Evaluate the integral. 40. 02|2x1|dxCh. 4.4 - Evaluate the integral. 41. 12(x2|x|)dxCh. 4.4 - Evaluate the integral. 42. 03/2|sinx|dxCh. 4.4 - Use a graph to estimate the x-intercepts of the...Ch. 4.4 - Repeat Exercise 43 for the curve y = 2x + 3x4 ...Ch. 4.4 - The area of the region that lies to the right of...Ch. 4.4 - The boundaries of the shaded region in the figure...Ch. 4.4 - If w'(t) is the rate of growth of a child in...Ch. 4.4 - The current in a wire is defined as the derivative...Ch. 4.4 - If oil leaks from a tank at a rate of r(t) gallons...Ch. 4.4 - A honeybee population starts with 100 bees and...Ch. 4.4 - In Section 3.7 we defined the marginal revenue...Ch. 4.4 - If f(x) is the slope of a trail at a distance of x...Ch. 4.4 - If x is measured in meters and f(x) is measured in...Ch. 4.4 - If the units for x are feet and the units for a(x)...Ch. 4.4 - The velocity function (in meters per second) is...Ch. 4.4 - The velocity function (in meters per second) is...Ch. 4.4 - The acceleration function (in m/s2) and the...Ch. 4.4 - The acceleration function (in m/s2) and the...Ch. 4.4 - The linear density of a rod of length 4 m is given...Ch. 4.4 - Water flows from the bottom of a storage tank at a...Ch. 4.4 - The velocity of a car was read from its...Ch. 4.4 - Suppose that a volcano is erupting and readings of...Ch. 4.4 - Lake Lanier in Georgia, USA, is a reservoir...Ch. 4.4 - Water flows into and out of a storage tank. A...Ch. 4.4 - The graph of the acceleration a(t) of a car...Ch. 4.4 - Shown is the graph of traffic on an Internet...Ch. 4.4 - The following graph shows the power consumption in...Ch. 4.4 - On May 7, 1992, the space shuttle Endeavour was...Ch. 4.4 - Evaluate the integral. 69. (sinx+sinhx)dxCh. 4.4 - The following exercises are intended only for...Ch. 4.4 - Evaluate the integral. 71. (x2+1+1x2+1)dxCh. 4.4 - The following exercises are intended only for...Ch. 4.4 - The following exercises are intended only for...Ch. 4.4 - The area labeled B is three times the area labeled...Ch. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Evaluate the indefinite integral. 7. x1x2dxCh. 4.5 - Evaluate the indefinite integral. 8. x2sin(x3)dxCh. 4.5 - Evaluate the indefinite integral. 9. (12x)9dxCh. 4.5 - Evaluate the indefinite integral. 10. sint1+costdtCh. 4.5 - Evaluate the indefinite integral. 11. sin(2/3)dCh. 4.5 - Evaluate the indefinite integral. 12. sec22dCh. 4.5 - Evaluate the indefinite integral. 13. sec3ttan3tdtCh. 4.5 - Evaluate the indefinite integral. 14. y2(4y3)2/3dyCh. 4.5 - Evaluate the indefinite integral. 15. cos(1+5t)dtCh. 4.5 - Evaluate the indefinite integral. 16. sinxxdxCh. 4.5 - Evaluate the indefinite integral. 17. sec2tan3dCh. 4.5 - Evaluate the indefinite integral. 18....Ch. 4.5 - Evaluate the indefinite integral. 19....Ch. 4.5 - Evaluate the indefinite integral. 20. xx+2dxCh. 4.5 - Evaluate the indefinite integral. 21....Ch. 4.5 - Evaluate the indefinite integral. 22. cos(/x)x2dxCh. 4.5 - Evaluate the indefinite integral. 23. z21+z33dzCh. 4.5 - Evaluate the indefinite integral. 24....Ch. 4.5 - Evaluate the indefinite integral. 25. cotxcsc2xdxCh. 4.5 - Evaluate the indefinite integral. 26. sec2xtan2xdxCh. 4.5 - Evaluate the indefinite integral. 27. sec3xtanxdxCh. 4.5 - Evaluate the indefinite integral. 28. x22+xdxCh. 4.5 - Evaluate the indefinite integral. 29. x(2x+5)8dxCh. 4.5 - Evaluate the indefinite integral. 30. x3x2+1dxCh. 4.5 - Evaluate the indefinite integral. Illustrate and...Ch. 4.5 - Evaluate the indefinite integral. Illustrate and...Ch. 4.5 - Evaluate the indefinite integral. Illustrate and...Ch. 4.5 - Evaluate the indefinite integral. Illustrate and...Ch. 4.5 - Evaluate the definite integral. 35. 01cos(t/2)dtCh. 4.5 - Evaluate the definite integral. 36. 01(3t1)50dtCh. 4.5 - Evaluate the definite integral. 37. 011+7x3dxCh. 4.5 - Evaluate the definite integral. 38. 0xcos(x2)dxCh. 4.5 - Evaluate the definite integral. 39. 0/6sintcos2tdtCh. 4.5 - Evaluate the definite integral. 40....Ch. 4.5 - Evaluate the definite integral. 41....Ch. 4.5 - Evaluate the definite integral. 42....Ch. 4.5 - Evaluate the definite integral. 43. 013dx(1+2x)23Ch. 4.5 - Evaluate the definite integral. 44. 0axa2x2dxCh. 4.5 - Evaluate the definite integral. 45. 0axx2+a2dx(a0)Ch. 4.5 - Evaluate the definite integral. 46. /3/3x4sinxdxCh. 4.5 - Evaluate the definite integral. 47. 12xx1dxCh. 4.5 - Evaluate the definite integral. 48. 04x1+2xdxCh. 4.5 - Evaluate the definite integral. 49....Ch. 4.5 - Evaluate the definite integral. 50....Ch. 4.5 - Evaluate the definite integral. 51. 01dx(1+x)4Ch. 4.5 - Verify that f(x)=sinx3 is an odd function and use...Ch. 4.5 - Use a graph to give a rough estimate of the area...Ch. 4.5 - Use a graph to give a rough estimate of the area...Ch. 4.5 - Evaluate 22(x+3)4x2dx by writing it as a sum of...Ch. 4.5 - Evaluate 01x1x4dx by making a substitution and...Ch. 4.5 - Breathing is cyclic and a full respiratory cycle...Ch. 4.5 - A model for the basal metabolism rate, in kcal/h,...Ch. 4.5 - If f is continuous and 04f(x)dx=10, find...Ch. 4.5 - If f is continuous and 09f(x)dx=4, find...Ch. 4.5 - If f is continuous on , prove that...Ch. 4.5 - If f is continuous on , prove that...Ch. 4.5 - If a and b are positive numbers, show that...Ch. 4.5 - If f is continuous on [0, ], use the substitution...Ch. 4.5 - If f is continuous, prove that...Ch. 4.5 - Use Exercise 65 to evaluate 0/2cos2xdx and...Ch. 4.5 - Evaluate the integral. 67. dx53xCh. 4.5 - Evaluate the integral. 68. e5rdrCh. 4.5 - Evaluate the integral. 69. (lnx)2xdxCh. 4.5 - Evaluate the integral. 70. dxax+b(a0)Ch. 4.5 - Evaluate the integral. 71. ex1+exdxCh. 4.5 - Evaluate the integral. 72. ecostsintdtCh. 4.5 - Evaluate the integral. 73. (arctanx2)x2+1dxCh. 4.5 - Evaluate the integral. 74. xx2+4dxCh. 4.5 - Evaluate the integral. 75. 1+x1+x2dxCh. 4.5 - Evaluate the integral. 76. sin(lnx)xdxCh. 4.5 - Evaluate the integral. 77. sin2x1+cos2xdxCh. 4.5 - Evaluate the integral. 78. sinx1+cos2xdxCh. 4.5 - Evaluate the integral. 79. cotxdxCh. 4.5 - Evaluate the integral. 80. x1+x4dxCh. 4.5 - Evaluate the integral. 81. ee4dxxlnxCh. 4.5 - Evaluate the integral. 82. 01xex2dxCh. 4.5 - Evaluate the integral. 83. 01ez+1ez+zdzCh. 4.5 - Evaluate the integral. 84. 01(x1)e(x1)2dxCh. 4.5 - Use Exercise 64 to evaluate the integral...Ch. 4 - (a) Write an expression for a Riemann sum of a...Ch. 4 - (a) Write the definition of the definite integral...Ch. 4 - State the Midpoint Rule.Ch. 4 - State both parts of the Fundamental Theorem of...Ch. 4 - (a) State the Net Change Theorem. (b) If r(t) is...Ch. 4 - Suppose a particle moves back and forth along a...Ch. 4 - (a) Explain the meaning of the indefinite integral...Ch. 4 - Explain exactly what is meant by the statement...Ch. 4 - State the Substitution Rule. In practice, how do...Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Determine whether the statement is true or false....Ch. 4 - Use the given graph of f to find the Riemann sum...Ch. 4 - (a) Evaluate the Riemann sum for f(x)=x2x0x2 with...Ch. 4 - Evaluate 01(x+1x2)dx by interpreting it in terms...Ch. 4 - Express limni=1nsinxix as a definite integral on...Ch. 4 - If 06f(x)dx=10 and04f(x)dx=7, find46f(x)dx.Ch. 4 - (a) Write 15(x+2x5)dx as a limit of Riemann sums,...Ch. 4 - The figure shows the graphs of f,f, and 0xf(t)dt....Ch. 4 - Evaluate: (a) 0/2ddx(sinx2cosx3)dx (b)...Ch. 4 - The graph of f consists of the three line segments...Ch. 4 - If f is the function in Exercise 9, find g(4).Ch. 4 - Evaluate the integral, if it exists. 11....Ch. 4 - Evaluate the integral, if it exists. 12....Ch. 4 - Evaluate the integral, if it exists. 13. 01(1x9)dxCh. 4 - Evaluate the integral, if it exists. 14. 01(1x)9dxCh. 4 - Evaluate the integral, if it exists. 15. 19u2u2uduCh. 4 - Evaluate the integral, if it exists. 16....Ch. 4 - Evaluate the integral, if it exists. 17....Ch. 4 - Evaluate the integral, if it exists. 18....Ch. 4 - Evaluate the integral, if it exists. 19. 15dt(t4)2Ch. 4 - Evaluate the integral, if it exists. 20....Ch. 4 - Evaluate the integral, if it exists. 21....Ch. 4 - Evaluate the integral, if it exists. 22....Ch. 4 - Evaluate the integral, if it exists. 23....Ch. 4 - Evaluate the integral, if it exists. 24....Ch. 4 - Evaluate the integral, if it exists. 25....Ch. 4 - Evaluate the integral, if it exists. 26....Ch. 4 - Evaluate the integral, if it exists. 27....Ch. 4 - Evaluate the integral, if it exists. 28....Ch. 4 - Evaluate the integral, if it exists. 29. 03|x24|dxCh. 4 - Evaluate the integral, if it exists. 30. 04|x1|dxCh. 4 - Evaluate the indefinite integral. Illustrate and...Ch. 4 - Evaluate the indefinite integral. Illustrate and...Ch. 4 - Use a graph to give a rough estimate of the area...Ch. 4 - Graph the function f(x) = cos2x sin x and use the...Ch. 4 - Find the derivative of the function. 35....Ch. 4 - Find the derivative of the function. 36....Ch. 4 - Find the derivative of the function. 37....Ch. 4 - Find the derivative of the function. 38....Ch. 4 - Find the derivative of the function. 39.y=xxcosdCh. 4 - Find the derivative of the function. 40....Ch. 4 - Use Property 8 of integrals to estimate the value...Ch. 4 - Use Property 8 of integrals to estimate the value...Ch. 4 - Use the properties of integrals to verify the...Ch. 4 - Use the properties of integrals to verify the...Ch. 4 - Use the Midpoint Rule with n = 6 to approximate...Ch. 4 - A particle moves along a line with velocity...Ch. 4 - Let r(t) be the rate at which the worlds oil is...Ch. 4 - A radar gun was used to record the speed of a...Ch. 4 - A population of honeybees increased at a rate of...Ch. 4 - Let f(x)={x1if3x01x2if0x1 Evaluate 31f(x)dx by...Ch. 4 - If f is continuous and 02f(x)dx=6, evaluate...Ch. 4 - The Fresnel function S(x)=0xsin(12t2)dt was...Ch. 4 - If f is a continuous function such that...Ch. 4 - Find a function f and a value of the constant a...Ch. 4 - If f' is continuous on [a, b], show that...Ch. 4 - Find limh01h22+h1+t3dtCh. 4 - If f is continuous on [0, 1], prove that...Ch. 4 - Evaluate limn1n[(1n)9+(2n)9+(3n)9+...+(nn)9]Ch. 4 - If xsinx=0x2f(t)dt, where f is a continuous...Ch. 4 - Find the minimum value of the area of the region...Ch. 4 - If f is a differentiable function such that f(x)...Ch. 4 - (a) Graph several members of the family of...Ch. 4 - If f(x)0g(x)11+t3dt, where...Ch. 4 - If f(x)=0xx2sin(t2)dt, find f(x).Ch. 4 - Find the interval [a, b] for which the value of...Ch. 4 - Use an integrai to estimate th sum i=110000i.Ch. 4 - (a) Evaluate 0nxdx, where n is a positive integer....Ch. 4 - Find d2dx20x(1sint1+u4du)dt.Ch. 4 - Suppose the coefficients of the cubic polynomial...Ch. 4 - A circular disk of radius r is used in an...Ch. 4 - Prove that if f is continuous, then...Ch. 4 - The figure shows a parabolic segment, that is. a...Ch. 4 - Given the point (a, b) in the first quadrant, find...Ch. 4 - The figure shows a region consisting of all points...Ch. 4 - Evaluate limn(1nn+1+1nn+2++1nn+n).Ch. 4 - For any number c, we let fc(x) be the smaller of...

Additional Math Textbook Solutions

Find more solutions based on key concepts
Show solutions
Testosterone Use Fueled by the promotion of testosterone as an antiaging elixir, use of the hormone by middle-a...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Evaluate the integral. 145xdx

Calculus (MindTap Course List)

In Exercises 1 to 6, find cos and cos.

Elementary Geometry for College Students

The acceleration for a particle whose position at time t is is:

Study Guide for Stewart's Multivariable Calculus, 8th

Sometimes, Always, or Never: dx equals the area between y = f(x), the x-axis, x = a, and x = b.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Determine 6.

Mathematics For Machine Technology

When Date Are Unevenly speed. If data are evenly spaced, we need only calculate differences to see whether the ...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6. The label on a 3-quart container of orange juice states that the orange juice contains an average of 1 gram ...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

In Problems 130 use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. 4. 1{(2s...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)