Exercises (4.8) Evaluate the following integrals (1) ſ sin3x sin2xdx (2) S sin3x cos2x dx (3) [ cosvx cos(sinvx) dx (4) S(sinx– cosx)²dx (5) S Vx cos²Vx dx (6) ſ cos³xdx

Q: | cos(In x) dx

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Q: Evaluate the following integrals: 1. S(cos x + csc² x)dx 2. S(tan x + sec² x)dx 3. S(1+sec²x)dx 4.…

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Q: 7. Evaluate the integral. J CoS X dx 0 1+sin2x

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Q: Evaluate the integral f sin²(3x) cos (3x) dx.

A: The given integral is ∫sin23xcos53xdx. We have to evaluate the given integral.

Q: Evaluate cos √6x dx using a substitution followed by integration by parts.

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Q: Evaluate the integral: Se3+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 - + C (3e)3 + cosh2x B…

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Q: Use MUPAD to determine the following indefinite integrals (7.1) (7.2) (2ax-x²)³ dx. S (7.3) Obtain a…

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Q: Q3. Use tabular integration by parts to evaluate the following Integral (x² +x+ 1) sin x dx

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Q: Integrate Each Using Various Integral Techniques 1.) S sin*(x)cos7 (x) dx Vx2-9 2.) dx, х>3 3.) S…

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Q: Evaluate the definite integral. sin x dx -dx J12 I+cos² x

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Q: Q: Find the integration for the following functions: - 1.- °(1-cos2x) 2-5 2- sin(tnx) dx 3-f-…

A: According to the guidelines issued by the company we are supposed to answer only first three sub…

Q: sin x dx | COS x 4/3

A: Integration of the function helps to find the required value of the given expression.…

Q: Determine the following integrals: 1.1 G 3x³ +8 X dx 1.2 G 1.3 4x+6 dx x + 3x-10 sec² (sin 5x)cos 5x…

A: We have to find out solution

Q: The suitable substitution to evaluate the integral V cos (2x) dx is COS

A: Given that:∫cos5(2x)csc3(2x)dx

Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x"-1 sin x…

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Q: Evaluate the integrals sin2.x -dp- J(5 + cos2.x) e) 3

A: Since, you have asked multiple question, we will solved the first question for you. If you want any…

Q: 3 Which of the following is equal to / sec 2 x tan³x dx to obtain the correct indefinite integral? A…

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Q: [3-v5 (2v7 dx sin(2x)

A: According to the definition, if dFdx=f(x), then ∫f(x)dx=F(x). The function f(x) is called the…

Q: Evaluate the integral. (Use C for the constant of integration.) 9x cos(8x) dx

A: Integrate this by integration by parts

Q: Which of the following integration expression can be transformed into integral of power 2 dx (A)…

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Q: 5e* dx d. J J1-e2x 1+cos (2x) е. sin2 (2x)

A: Using the substitution method and solve the integration explanation is given below...

Q: Find the integration: J* 1+sin X 4 dX Cos 2X

A: Introduction: Suppose, fx is a continuous function on the interval a,b. There is another…

Q: Evaluate the integral. (sin Sx cos 5x dx 늘 cos 13x-5 cos 3x + C 26 1 cos 13x - 26 1 sin 13 x + C 26

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Q: Use integration by parts to evaluate the integral. 6 3 e cos x dk 0

A: Given integral is

Q: In integrating the function f(3x + 5)(cos) dv using integration by parts, what would you choose for…

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Q: II. Evaluate the following integrals: 7 ax 52X+7 13. [ sin x 2 - cosX (1x dx 14. S MA sec² 3x -dx 1…

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Q: Q6. A: Evaluate the integrals: sec x dx dx 2) L, | VIn(secx+ tan x) -2 (4+x²)3/2

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Q: 1) Evaluate the integrals: (a) f sin³ (2x) cos (2x) dx (b) sin³ (2x) cos (2x) dx

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Q: Evaluate the Integral dx – (**V2Tan-1x-(Tan-1x)2 1-х4 '2Tan-1x-(Тап-1x)2 3. S х?/2Tап-1x- (Тап-1x)2…

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Q: 7. Use integration by parts to prove that for any positive integer n, | cos"x dx = 1 cosn-1xx+ n - 1…

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Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x*-1sin x…

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Q: subparts d,e,f

A: (d)Consider the given integral:

Q: Evaluate the following integrals. 1. dx 3p3 2. [rvx-4 dx 3. [xvi+x dx 4. [ 1-3х dx V2x-3x 5.…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Use integration tables to find or evaluate the integral ∫ 1 / sin   x cos   x dx

A: We have to evaluate the integral: ∫1sin x cos xdx We know the identity: sin2x+cos2x=1 Substituting…

Q: Evaluate the integral / cos (r) sin(x) dx 16 COS using the substitution u = cos(x). ,16 cos" (x)…

A: This question is based on indefinite integral.

Q: Evaluate the integral. • T/3 L 3 sin° ( 3x ) dx Зx) dx

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Q: Evaluate the integral 1 2 (5e Vx - sec 2) dx. ух е XM

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Q: Which of the following integration expression can't be transformed into integral of power 2dx A 4+3x…

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Q: Evaluate the integral. (Use C for the constant of integration.) 3 cos x dx 6 + sin x

A: Evaluate the integral.

Q: Evaluate the integral (i) S3x3 sin 4x dx (ii) ſ In (x³ + x) dx (ii) cot-1 2x dx (iv) ſeax cos bx dx

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Q: -1 sinx dx %3D

A: ∫01/2arcsin(x) dxIntgerate by parts ∫fg=fg=∫f'gf=arcsin(x),…

Q: Perform the following integration. 1. (sinhr) (coth² x + csch³ x) dx sec³ x tan x 2. S dx √2 + sec x…

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Q: f sin-¹(x) dx

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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: Evaluate the integrals: (d) ∫(lnx)2dx. (e) ∫tan−1(3x)dx. (f)∫cos4(3x)dx.

A: We can evaluate the first two integrals by using  the integration by parts method. To evaluate…

Q: b) By using integration parts, show that ii. S(3x + 5) sin(2x + 3)dx = -÷(3x + 5) cos(2x +3) +sin(2x…

A: By using integration by parts, show that∫3x+5 sin2x+3 dx=-123x+5 cos2x+3+34 sin2x+3+C

Q: Evaluate the integral. (Use C for the constant of integration.) cos(x) (4 + 8 sin²(x)) dx

A: Solve the intregal

Q: Use U-Substitution to evaluate the definite integrals. Sž cos 2x dx (1+x2)2

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Q: (x² sin(x')dx = 3 %3D

A: Given : Integration of X2sin(X3)dx