Q4: a)Evaluate the integral: ( In(cosh2x) coth2x dx b) prove that sec-1x = cos-1! = Cos

Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: Express lim Σ n → ∞i=1 3 n ( n 3i + COS 9/² 2 as a definite integral

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Q: 5) find the integral J8 sin 2x * cos2x dx

A: see below the calculation and answer

Q: (2- sec?x) " sec(3А — х) e In (a le) sec3x -dx to be integrable using What should be the value of A…

A:

Q: Use the tabular method to evaluate the integral - 2x – 1) cos(4x)dx

A: Introduction: Tabular integration is a technique for quickly integrating many parts in a row. One of…

Q: •2 dx

A:

Q: Evaluate the integral. |cos 7x cos 3x dx

A: The given integral ∫cos7xcos3xdx.

Q: sin 0 -do 4+cos 0 Evaluate

A: Since 4+cosθ is never zero in 0 to 2π as -1≤cosθ≤1. So, 3≤4+cosθ≤5 So, sinθ4+cosθ is analytic in 0…

Q: Evaluate the integration 2.5 o cos(x) with h=0.5 by using 3/8 Simpson Rule. Write your answer in 4…

A: The Simpson's 3/8 rule states,∫ydx=3h8y0+2y3+y6+ . . . + yn-3+3y1+y2+y4+y5+ . . . +yn-2+yn-1+ynWe…

Q: Use integration by parts to show that for n > 2: / sin" x dx: 1 sin- x cos x + /sin-2 x dx.

A: To evaluate: ∫sinnx dx

Q: Use integration by parts to show that, for n > 2, 1 cos a sin"-1 n 1 sin"-2 xdx. n - sin" xdx = x +…

A:

Q: (5) Find the indefinite integral (a)f Vtan x sec²dx (b)fem2* sec² 2xdx sin x (c) Cos x 1 cos-do 0 2

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Q: Evaluate the integral: 25 tan² 12x dx Choose the most appropriate answer. tan3 3 12x O 25 × 1 12 ln…

A: Explanation of the answer is as follows

Q: 14. Verify that f cotx dx = In(sin x) +C. (Do not try to solve the integral from scratch.) %3D

A: Given: verify that ∫cotxdx=lnsinx+c For verifying given integral, we integrate given integral

Q: 3. Solve the integral by two grid in the y-direction and four grid in the x-direction with…

A: Solve the integral by two grids in the y axis and four grids in the x axis with Trapezoidal rule:…

Q: 5. Evaluate the indefinite integral. S cososin'oc (1) (3x - 2)20 dr (2) (3) S etanr sec?rdr

A:

Q: Show that sec x = (sin x / cos x) + (cos x / 1 + sin x), then use the identity to drive the basic…

A: (i)…

Q: Evaluate the definite integral 3 2 sin (2)dx using Part 1 of the Fundamental Theorem of Calculus. 57…

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Q: Find F'(x), where F(x)= int. of ((t^2)+1)dt, from sin(3x) to x=-4. Use the 1st rule of the…

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Q: Use the methods of (1) left Riemann sum, (2) right Riemann sum, (3) trapezoidal rule, (4) parabolic…

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: dx so that the resulting integral is integrable? What should be the rewrite of the integrand of…

A:

Q: Which of the following is equal to sec 2x tan³x dx to obtain the correct indefinite integral? A x-…

A: The given integral,        ∫sec32x tan3x dx

Q: Find the trigonometric integral. (Use C for the constant of integration.) (cos(20))(sin(0) +…

A:

Q: By Cauchy's integral formula show that, Se" esin e -2n cos(cose) de = 2n; "esine sin(cose) de = 0 0,

A: Cauchy's integral formula : Let U be an open subset of the complex plane C, and suppose the closed…

Q: 10. Prove by using integration by change in variable the ff. integral: dx du = arcsec x + C xVx2 - 1

A: To show∫dxxx2-1=sec-1x+C.

Q: What is the integral of 10pi(4-y)(sqrt(siny))dy from 0 to pi?

A: Let I=∫0π10π4-ysinydy Then, ∫0π10π4-ysiny…

Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: Evaluate the integral.  integral  sec 2 x  tan x  dx

A: Given: I=∫sec2xtanxdx for evaluating given integral, we substitute tanx=t…

Q: the integral of tan^5 (x) sec^3 (x)dx

A: we will find integral  of f(x) using rule as mentioned above

Q: Consider the integral f sin-1x dx. If we let u = sin-1x and dv = dx, the integral can be written as…

A:

Q: Evaluate the integral S cos ³ x + 8 sin x cos³² x + 6s in ² x dx; cosx #0 2 cos²x

A:

Q: The value of integral cos (1+x) d, n= 4 by Trapezoidal rule is (up to 4 decimal digit) Answer:

A: The trapezoidal rule can be used to calculate the integral numerically. The formula for the…

Q: /2 cos x -dx- 1+(sin x)? Compute the integral

A: Consider the following definite integral: ∫0π2cosx1+sinx2dx Substitute sinx=u→cosxdx=du in the above…

Q: What is the integral of (2 sec^2x - sinx) dx? * 2 tanx + cosx + C 2 cosx + tanx + C 2 sinx + cosx +…

A: Explanation: Given that: ∫2sec2x-sinxdx Concept used: ∫sec2xdx=tanx+C∫sinx       =-cosx+C

Q: Evaluate the integral. (Use C for the constant of integration.) 7 (1 – tan²c«) dx sec?(x)

A: NOTE: Refresh your page if you can't see any equations. .

Q: (b) 3 – cos(x) 2

A: Follow the procedure given below.

Q: Evaluate the integral. integral   sec 6  t  / tan 3t dt

A:

Q: Evaluate the indefinite integral.

A: It is required to evaluate the indefinite integral:

Q: Find the product of the integral ri sec²(cos(x))dxdy sin-y

A: Given ∫01∫sin-1yπ2sec2cosxdxdy

Q: 4 -dx is divergent. 1-2х (b) Show that the improper integral

A:

Q: Evaluate the integral. sec 0(sin 0 cos 0 + cos 0) de Jo

A: Let I=∫0π/2secθsinθcosθ+cosθdθ

Q: dt cos°(2 sin" 21)/1– 4r cos(2 sin2t

A:

Q: 0.5 cos x In(3 sin x)dx = COS I %3D 0.1

A: Definition used -   U substitution - When there is a composite function multiplied by the…

Q: Evaluate the integral. dx JSlx2 - 3 sin 1 33 x + C 3 sec1 |9x - 3| + C sec 1 19 x| +C * sec 13/5 x|…

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Q: Use integration by parts to evaluate the integral: far Ar cos(- 6r)dr

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Q: Evaluate the integral. T/3 7 sin(0) + 7 sin(0) tan²(0) de sec²(0)

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Q: Use integration by parts to evaluate the integral: sin( – 8r)dr - 05 e-r(sin(-8r) - 8 cos (-8r)) + C

A:

Q: 5. Use integration to find the exact area outside r = 4 cos 0 and r = 4 sin 0 but inside r = 2.

A:

Q: Solve the integral by two grid in the y-direction and four grid in the x-direction with Trapezoidal…

A: The given integral is: ∫45∫23xcosydydx Here  x0=4, x1=5y0=2, y1=3fx,y=xcosy By Trapezoidal rule,…

Q: Which of the following leads to trigonometric integral formula of integration? cscx sin2xdx (…

A: Given, Which of the following leads to trigonometric integration formula for integration: