Question 007: Complete the following question involving Substitution Methoc Given the integral | 4sin(8x + 11) dx and the substitution information u- 8x + 11 u'- 8 dx Plug the information into the integral, simplify, and then work out the integral. 1 으cos(Bx + 11) 으글.cos(Bx + 11) + C 2-sin(8u) + C -1 ㅇ글sin(8x + 11)+C

Q: 3. The integral of sin24x cos4x dx is a. (1/4) sin³ 4x + C b. (1/3) sin³ 4x +C c. (1/12) sin³ 4x+ C…

A:

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

A: see below the calculation and answer

Q: Evaluate the integral: cos 4x cos 6x dx. A) sin 2x + sin 10x + c. 20 -sin 2x + sin 10x + c. C) sin…

A: Let's find integration of given function.

Q: Evaluate [(1 +x-3 + sin4x)dx -2 cos4x X - + c 4 0x-- cos4x + C cos4x O 2x- 4 0 4x-두-5t +c cos5x + c…

A: As we know that the integration of : ∫fx±gxdx=∫fxdx±∫gxdx ∫xndx=xn+1n+1+c ∫sinxdx=-cosx+c

Q: 2. Evaluate the integral ſcos (3x) sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

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Q: Which of the following is one of the correct steps to evaluate cos3 dt to obtain the correct…

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Q: Evaluate the integral. π/2 sin³ 0 cos²0 de 3

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Q: Watch the video on the integral of sin(ax)cos(bx) and the video on the p two cosines with different…

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Q: 5) Integrate 2x cos (x²-5) with respect to x.

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Q: 2 2 In sin 2x - 2 In (1 + cos 2x) = In ( )- %3D

A: Given that: The identity is 2 ln sin 2x - 2 ln ( 1 + cos 2x) = 2 ln tan x .

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: Chapter 6, Section 6.3, Question 012 Use the Fundamental Theorem to evaluate the definite integral…

A: Given,

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A:

Q: uestion 4. Evaluate the value of the integral 2. COS cos (30) dr. 5- 4 cos(20) 2x

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Q: 82. Show that cos at cos bt %3D In

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Q: The value of integral (cos(4x)+cos(81)) dx

A: We have to determine the integral

Q: sin (21 + 1) dt J cos² (21 + 1)

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Question 004: Complete the following question involving Integratin by Parts Method. Given the…

A: the given integral is ∫4x*sin5x dx and the substitution information is: u=4xdu=4dxv=-15cos(5x) we…

Q: Chapter 6, Section 6.3, Question 014 Use the Fundamental Theorem to evaluate the definite integral…

A: Given,

Q: (1+ etane) sec² e de = e TO FO 2 [0(sin(In 0) + cos(In 0))] = de csc(ln 0)

A: ∵1     ∫0π4(1+etan θ) sec2θ dθ=∫0π4(sec2θ+etan θsec2θ )dθ=∫0π4sec2θ dθ +∫0π4etan θsec2θ dθ∵∫0π4sec2θ…

Q: tan 2x – 1 dx. 5 tan 2x + 5 Q5: Determine 1 In |sin 2x + cos 2x| + C 10 A 1 В In |sin x + cos x| +C…

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Q: Evaluate the integral. 7/2 cos 6x dx COS -T/2

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Q: The integration expression sin(3In(x) + 4)cos(3ln(x) + 4)dx must be transformed into using suitable…

A:

Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: This question has several parts that must be completed sequentially. If you skip a part of the…

A:

Q: Solve the integral of 2sin(x)/(1+cos^2(x)

A: We have to solve the integral.

Q: Evaluate the integral: 20 cos(20x+3) dx 23 sin (20x+3) Choose the most appropriate answer. Sin3 69…

A:

Q: Prove That 4 Sin ³²A - CoS 3 A +4 Cas³ A - Sin 3 A = 3 Siny A

A: We need to prove: 4sin3A.cos3A+4cos3A.sin3A=3sin4A

Q: Find the indefinite integral. [ cos 3xar sin33- sin 3r +C 6. O sna(3- sn'ax) sin3 3-sn 3 +C sn3x…

A:

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: .2 1 2x -1 Prove that : sin .2 dx = 72 1+x 1+x?

A: Solution of given question is given step by step

Q: 13. (2х + 1) sin 4x dx; и — 2х + 1, dv %3D sin 4x d 14. х cos 4x dx; и %3D х, dv 3D сos 4x dx

A: 13:      ∫(2x+1) sin4x dx                14:      ∫x cos4x dx

Q: 8. 6x° cos (x³) dx

A: ∫ x8cosx3dx

Q: Evaluate the integral: 3 X sin ³ COS 3 3 X col 3

A: Solved below.

Q: 7) Evaluate the indefinite integral / cos cos 2t sin 2t dt.

A:

Q: Scos cos 3x -1+ cos 5x - dx

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Q: sin 70 do 9+ cos 70 Evaluate the integral ; using the substitution u = 9 + cos 70. sin 70 do 9+ cos…

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Q: ☆ 6. Find the integral of xx²-1 O Sin ¹x + C 4 O Sec-¹x + C Cos ¹x + C Sec-1 (1)

A: Here we have to find the integral.

Q: Chapter 6, Section 6.3, Question 013 Use the Fundamental Theorem to evaluate the definite integral…

A: Consider the integral

Q: 2. Evaluate the integral J cos (3x) sin°(3x)dx in two ways, one with u = u = cos(3x). Even though…

A: Given: Apply u-substitution method. Use two methods u=sin(3x)  and u=cos(3x)

Q: cos(9x) -dx COS J 1+ sin²(9x)

A:

Q: Which of the following is one of the correct steps to evaluate cos³ dt to obtain the correct…

A: In this we have to find which of the following correct steps to evaluate the given Integral.

Q: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

A: The given integral is: I=∫2sin3xcos2xdx   As we know that; The trigonometric identity; sin2x+cos2x=1…

Q: Chapter 6, Section 6.3, Question 009 Use the Fundamental Theorem to evaluate the definite integral…

A: Consider the given integral.

Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

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Q: 5) Determine the following indefinite integral cos (3x) (1 – sin(3x))(2 – sin(3x)) -dx

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Q: 26 csc (2x) cot(2x) dx (Use Substitution Method) 26 26 + C 4 sin (2x) 4 2 26 26 + C 4 sin? (2æ) 4 26…

A: Integration.

Q: Question 6 Compute the following integral: sin (8z) de 1 4 a) cos(8x) sin*(8x) + C 32 1 cos (8r) + C…

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Q: tan Find the integration of 1₁ 1+z²

A:

Q: 2. Prove that cos30 = (4cos'e - 3cos0) and sin30 = (3sine – 4sin e) using De Moivre's Theorem. %3D…

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