Evaluate the integral. x/2 | [3 cos 5t i- sin tj+ sin? 8t k] dt x/2 | [3 cos 5t i - sin tj+ sin? 8t k] dt = (Di+ Di+ O k (Type exact answers, using x as needed.)

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A: Here we consider the following we find a substitution rewrite the integrandterm e8x as…

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A: The objective of the question is evaluate the indefinite integral by using substitution .

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A: Topic-. Integration.   Note - as per our guideline only first three subparts to be solve others can…

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A: To evaluate the following integral by using Walli's formula.∫0π2 sin4 x cos4 x dx

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A: Since you have asked multiple questions in a single request, as per policy, only first question is…

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A: We have to evaluate the integral is ∫cx+ydx+y−xdy. where c is given by x=cosθ, y=sinθ and 0≤θ≤2π.…

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A: 1a): Given integral is: I=∫dx(2x+1)4x2+4x=12∫dx(2x+1)x2+xLet…

Q: Q3. Evaluate the following Integrals Stan? 0 sec? e de | cos 7x cos 2x dx 4sin3x dx 1+cosx Q4.…

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A: We know that integration of xn is nxn-1.   Here i attached the solution of this question.

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A: To evaluate the given integral.

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A: We can rewrite the given integral by using this substitution u = x1/2

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Q: 1. Evaluate the iterated integral: r12 Jo o cos(2) dy dx. -

A: To find ∫π2π∫0x21xcosyxdydx: First solve ∫0x21xcosyxdy: Let u=yx  dudy=1xdy=xdu…

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A: Given: The given integral is ∫15x2-x3-43x-19x+12x2-6x+13

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Q: Evaluate the integral using the given substitution. Sx cos (10n2) dx, u = 10x² sin (10x²) - C sin…

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Q: Evaluate the integrals

A: We have to evaluate ∫0π1-cos2θ dθ We know that sin2θ+cos2θ=1 ⇒ 1-cos2θ=sin2θ Therefore,…

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Q: Q1) A-Evaluate the following integrals: 1) S (cos x / sin? x) dx. 2) S (2x+4)/3 dx, use x-0 to x-2.…

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

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A: Given : ∫0a3  3x2cosx3dx , where a is some positive real number

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A: (a) For, Is non elementary since y is in denominator. (b) For Is non elementary since x is in…

Q: Which of the following is an improper integral? A) In(1+x*)dx -dx -4 x² – x – 2 В dx C 2x + 8 C…

A: Given A.∫-10ln(1+x4)dxB.∫-40xx2-x-2dxC.∫2612x+8dxD.∫-2ln(3e)xecosxdx

Q: Evaluate the integral using the given substitution. Jx cos (5x?) dx, u=5x? O A. sin (5x2) +c 1 O B.…

A: Note:Since you have asked multiple question, as per our guidelines we are supposed to answer only…

Q: Consider the following indefinite integral. 6x3 + 5x² – 47x – 36 dx x2 9. The integrand decomposes…

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Q: Given: J5x2 cos(3x³) dx. If U=3x°, then the resulting integral is Jf(u) du. Find 4

A: I=∫ 5x2 cos(3x3) dxu=3x3du = 9 x2 dxx2 dx =du9which gives;I =∫ 5 cos(u) du9I =∫ 59cos(u)  du…

Q: Evaluate the integral e'sin e) dx 1- In 2 2 u +3 u + C + C +C cos(e") + C COS -2*+2x + C 21 21

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Q: Determine the following particular integrals: -{3x²e-x} 2.1 2.2 1 D² + D-1 1 D² - D+2 {8 sin x cos…

A: To Determine: the following particular integrals:   2.1 1D2+D-13 x2 e-x 2.2  1D2-D+28 sinx cosx

Q: Compute the following integrals (i) I = f 8(9- 10x? + x*) cos(Tx) da. (ii) I = S 6(x(1 – a?)) x (1–…

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Q: What is the integral of x" cos ax dx ? хN sin ax А. -=S nx"-1 sin ax dx + а а хN sin ax B. n -"Sxn-1…

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Q: 11. The integral of nunex dx is bln]sec(In(2x)")|. What is b? A. 2 B. 2 C. 4 D.

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Q: -Jxcar (r<)= o x sin(ñ x) cos (Tx)

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Q: Evaluate the integral using the given substitution. SV cos (2-7) dx Select one: 3/2 sin (x - 7) + C…

A: topic - indefinite integral

Q: Evaluate the integral below. cos(y) dy dx /x/3 Select one: O a. sin 1 O b. O O c. 1 O d. sin 2 – 1 O…

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Q: of the following is an improper integral? • In3e COsx dx xe | in(x*+1) dx n(x++1)dr -4 x2-x- 2

A: Improper integrals are characterised as

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Q: Which of the following is an improper integral? -4 x² – x – 2 In3e COSX dx xe -2 In(x++ 1) dx -1 dx…

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Q: Find the integral ſ cos³0 sin 0 d0 . Tentukan integral f cos³0 sin 0 de. 1 cos*0 + C 4 1. O 1 -coste…

A: Let's find.

Q: Which of the following is an improper integral? dx A 2x+8 cos (x)dx B -2 C -4x2-x-2 In(1+x*) dx -1

A: Improper integral is the integral in which function approaches to Infinity within in the given…

Q: The resulting integral of S dx is In + e Tan"1+ C where a, b, d, and e are integgrs. x+x²+4x+4 What…

A: Differentiate the result of the integral:…

Q: (a) Solve the following integrals. (i) (ii) x' + 3x? – 10 - dx x(x – 3)(x+1) Integrate er* cos (3x)…

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

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Q: Which of the following integrals is equal to the integral / f(3x – 5) dx? 7/3 zP (?)f s(2) dz 2. 7/3…

A: Topic = Integration

Q: Evaluate the integral V16 – x2 O A.8 sin-1(프) - 특V16-22 +c O B. sin-1(플) + c O C.8sin-1(플) - n. V16-…

A: Option (a) is correct.