(a) Use an appropriate substitution to integrate the following. V1+4x (b) Use a trigonometric substitution to evaluate the following integral. S sin³ x cos² x dx

Q: 38. Solve the integral / x³ /x² – 1 dx three ways: (a) with the substitution u = x? –- 1, followed…

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

Q: 1 So x2-4 dx an improper integral. (5 points each) 3. Find a value of b >0 that makes

A: Given the function :

Q: 1. Evaluate the following integral using trigonometric substitution. dx x>3 Vx² - 9 dx Vx² - 9 (Type…

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Q: 1. Solve the following integral by using the Integration by Parts. (a) x sin x dx (b) e 2x sin 2x dx

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Q: a) If | f (x) de f(x) dx = 2, find 1 (3f(a) – 1) de. = 7 and || - /4 (b) Estimate the value of the…

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Q: The resulting integral of sin-cos-sin0 de 2 2 has the form -F(0) - +C. What should be the value of e…

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Q: Q2 (a) Calculate each of the following integrals. sin 3 0 cos'e 1 S sin x(cosx)4 dx

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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: 1 /- To evaluate the integral dx, using a trigonometric substitution, which substitution should you…

A: Evaluating integral by trignometric substitution

Q: Question 1. Evaluate the following integrals using substitution method: |(x-1)(x²–2x)"dx_ a) sin°…

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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: Q: 1. (a) Use an appropriate technique to evaluate the integral dx (2x + 1)v4x2 + 4x (b) Evaluate…

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

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. dx…

A: We have to find the integral

Q: Q2 Find the integral for the following : dx 1 1-5 2- fe-*sec? (ne-*)dx 3- S dx 2vx+2x 1+e*

A: We have to find the Integral for given expressions. 1. ∫dx/(2√x + 2x)  2. ∫e-x sec2(πe-x)dx  3.…

Q: Using an appropriate substitution, (cos-1(x)) e the integral f dx equals: V1-x2

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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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Q: Which of the following is one of the correct/convenient steps to evaluate cot-+dx _which will yield…

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Q: C for the constant of integration.) Evaluate the definite integral. (Use sin(23x) xp 1 + cos (23x)…

A: The given integral is,

Q: x 4 dx (x²+4)² S

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Q: ! Using an appropriate substitution, the integral dx 36-(2x + 2)² is equal to sin-¹(x + 1) + C the…

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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: a. b. Evaluate the following integrals 2 dx cos²x√4 tan x- tan² x I [ sin(√a)da dx

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Q: 1. Find the general indefinite integral. 5e + 3 sin x dx (b) ["be²

A: We have to solve this given integral . For this first we solve the general indefinite integral &…

Q: Use the value of the first integral I to evaluate the two given integrals.

A: It is given that, I=∫0π/2cosθ-2sinθdθ=-1 Consider the integral ∫0π/22sinθ-cosθdθ

Q: 3. a. b. Evaluate the following integrals 2dx dx cos²x√4 tanx - tan² x sin(√x)dx J I sin

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Q: Question 2 Evaluate the following integrals using the appropriate rules of integration. 2.1 S(cos x…

A: (2.1) Given- ∫-π2π2cos x-1 dx To find- Evaluating the above integral using appropiate rules of…

Q: 3. Evaluate (using appropriate substitutions if necessary) the following definite Integrals. (a) ,…

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Q: dr Evaluate the integral / dx. sin x cos x

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Q: 4. Evaluate the following real-variable integrals using the method of residues: 2 cos (0) Jo…

A: PART A Consider ∫02πcos2θsinθ+2dθ Let us assume : dz=eiθi dθdz=iz dθdziz=dθ

Q: Evaluate the following by changing the order of integration: 4 4 cos(y²) dy dx. 2.

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Q: Evaluate the following integral.

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Q: dx x* +3

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Q: Q4: Find the integration for the following functions: - (answer three only) sin(lnx) dx 3-…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 2. Using an appropriate method, compute the following integrals. dx x² + 3x + 2 (i) sin³x cos*x dx…

A: (i)

Q: Find the most general antiderivative or indefinite integral. 2. cos 7x - csс"x) dx

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Q: Given SV-x* + 4x + 5 dx. Using trigonometric substitution, what is the integral form in terms of 8?…

A: Trigonometric identities: sin2θ+cos2θ=1cos2θ=1+cos2θ2 If an expression is x2+bx, then we need to add…

Q: Using the trigonometric substitution, the integral dx (x2 - 16) Vx2 – 16 I = is equal to the…

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Q: 1. Evaluate the trigonometric integral. (1) [20sin² (2x)cos (2x)dx (ii) S4ta dt

A: Given integral is: I=∫20sin22xcos22xdx To solve this integral we will use the following…

Q: Step 2 1 To find the integral S H x cos 8x dx by the parts formula, use u = x and v = Apply the rule…

A: This is a problem related to integration. Based on the general formula of integral by parts we will…

Q: Find the indefinite integral ∫ dx / (4 + x)3/2 (a) using a table of integrals and (b) using the…

A: a) ∫dx4+x32 Apply u- substitution : u=4+x du=dx plug all this values in given integral and then…

Q: 1 To evaluate the integral dx, using a trigonometric substitution, which x2 + 6x + 13 substitution…

A: Make the denominator in standard form than do the substitution such that integration become simpler.

Q: cos5 0 sin 20 de

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Q: 1. Evaluate these integrals either by substitution or by integration by parts: cln 2 et a sin(2r) dr…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: -cos-sino de has the form sin 2 2 -F(0) +C. What should The resulting integral of 4 be the value of…

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Q: S. The resulting integral of sin cos-sino d0 has the form | 2 2 -F(0) + C. What should be the value…

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Q: Q;: Find the integration for the following functions: - (answer three only) In(x²+x)-Inx-e!nx 3-S-…

A: Given  1) The integration is  -∫π01-cos(2x)2dx .

Q: 1. Perform the integration. Show all necessary solutions. 8t² + sin t sint + cos ty dt co t

A: Find your answer below

Q: (b) Find the following integrals: i. f(4x³+ sin x) dx. ii. ₁²(x²+)dx.

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Q: Q.4 Use the integration by parts to evaluate the integral. V3 2 sin-1 x dx

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