4 In |x=3| The improper integral dx can be written as: x-3 Select one: 3 In(3-x) dx 4 In(x-3) dx a. x-3 х-3 O b. 3 In(3-x) dx + J. 4 In(x-3) dx x-3 x-3 C. None of these O d. 3 In(x-3) dx + J, 4 In(3-x) dx х-3 х-3

Q: Find the integral: x2-2/x+1 dx choices: a) x2/2 - x - In(x+1) + C b) x2 - x - In(x+1) + C c) x2…

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Q: Еxercise: 1- Use the Composite Trapezoidal rule with the indicated values of n to approximate the…

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Q: Evaluate the iterated integral. 4 (x² - y²) dy dx -4

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Q: The improper integral 1 dx is 'o 2V1-x²

A: this can solve simply by apply the integration formula

Q: Which among the following is an improper integral? -0.5 dx a. O5- -0.5 1-x2 csc?x b. Si dx V5-csc2x…

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Q: 3) The Integral x In x dx (a) 2ln2 (b) 4 In4 (c) o (d) 1

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: 1. Compute the following integrals. 1 cos 3x dx b) VAr + 7 c) a) dx dx sin x / (In x)3 f) / d) ſ eª…

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Q: Evaluate the following integrals Li l2l e(1+x²) dx i.

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Q: 7. Evaluate the following integrals using the multipi -3 xy dx dy (1i) ye* dx dy (i) y e* dx dy

A: To evaluate the given double integrals.

Q: 4. Evaluate the integral 2+ In? x -dx. x – x ln x (a) 3 ln |In a – 1| + 2(ln r – 1) + (In a – 1)2 +…

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Q: 1. Find a particular integral for d²y dy dr +4- + 3y = r? dr2

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Q: 1. Evaluate the improper integral or show that it diverges. (a)/ e* dx 8. (b) / dx (c) d.r (d) /…

A: If the limit exists and is a finite number , we say that the improper integral converges .If the…

Q: Evaluate the 2 improper integrals attached with this question.

A: Given integrals are

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A: topic - triple integration  answer is ln(64) =6ln(2)

Q: Find the integral *-15 dx. x +1 a. 15In(x² +1)-arctan(x) +C 1 – 15 arctan(x) +C 15ln(x² +1) 1 + 15…

A: i will use substitution method to solve this.

Q: To apply the integral test for 3n2 + 1 n3 +n n=1 we evaluate the improper integral 0 3x2 + 1 dx. x3…

A: Solve the following

Q: For x 1/2 -dx and using the substitution u=x 1/2, the resulting integral takes the form: x-x 4u -du…

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

Q: Find the integral. J 3 x√9 - (In x)² + C dx

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Q: 2. Set up and evaluate the integral for L»e-² + x) dA where D is the shaded region shown. (1, 2)…

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Q: What is the area between y = √x + 2 and y=-3x + 6 from x = 0 to x = 1? Select one: O a.-x² + 4 11 6…

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Q: 14. Find the equivalent integral of * S x(x+1) O-f3dx + f 3d x+1 dx OS÷-1# R x+1 01 Of //dx -…

A: Here we have to apply partial fraction.

Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

Q: Which of the ff is equivalent to the double integral: a. f¹ ln(2x) − In(x + 3) dx b. ln(x + y) -…

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Q: 9. Evaluate the following integrals. Show all work. a) Se"(e* -e* )dx dx b) 13-2x 3-2х c) dx sin 3x…

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Q: A. Evaluate the following integrals. 1s (*2* -) x, 2х — 3' dx + 1. S x+2

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Q: 39. Use a software application to compute the integrals у — х dx dy (x + y)³ у — х dy dx Jo (x + y)³…

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Q: Which of the following is NOT an improper integral? 0 2x of ₁7² +²22-3²² dx + 2x - 3 2x x2 2 - 3x e…

A: which of the following is not an improper integral??

Q: Evaluate the integral. | (In(3.x))² dx = +C

A: From the given problem: I=∫ln3x2dx  ....(1) Let, t=3x So, ddxt=ddx3xdtdx=3dx=13dt Nw substitute…

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: Evaluate the following integral. In 2 z In (3y) ex+y-z dx dy dz 1 In (2y) In 2 z In (3y) e**y -z dx…

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Q: Which one of the following is a PROPER INTEGRAL? OA. .5 2x dx. 3 7x2-3x O B. dx. x In Oc. | x2…

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Q: 3. Find the integral * dx a² -2 x+1 a.-x - - x - In(x + 1) + C 2 b.x2 – x – In(x + 1) + C c.x2 – x +…

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Q: Evaluate the improper integral A 0 (B 4 C diverges 2 D 9 mit 2 3 -2 X 3 dx

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Q: 2. Calculate the following transcendental integrals: a) S² exee* dx X b) S (x²+1)In (x²+1) dx cos…

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Q: Which one of the following double integrals is equivalent to the integral 2x-x2 Vx2 + y2 dy dx? 0.…

A: The integral in Cartesian coordinates is : We first try to look at the region of integration here:…

Q: Evaluate the Cauchy principal value of the given improper integral. 1 [ (x² + 4)² dx

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Q: evaluate the Cauchy principal value of the given improper integral. roo 1 dx 6x + 25 | roo x2 dx (x2…

A: The Cauchy principal values of the given improper integrals areevaluated as shown below.

Q: Evaluate the following sum of iterated double integrals: 1 2y r2 r4-2y dz-a dx dy + Ax-a² dx dy e…

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Q: accordingly, if the order of the integral given above is changed to dyd dx, what will the integral…

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Q: One of the following is an improper integral. cln 3 e* dx dx J, xV16 – In x In 2 V4 - ex In 2 CA dx…

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Q: The improper integral A B if the 0 1 0 e dx is

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Q: 2. Evaluate the fellowing Integrals:- e dx dx ans (z a.

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Q: Evaluate the following integrals where n 0,1,2,... n even 1) sin(nx)dx Ans. 2/n n odd 2) Jasin(nx)dx…

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Q: Evaluate the integral of ((x dx)/(x + 1)8) from o to 1.

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Q: The result of the integral dx (x + 2)(x + 1) is equal to Select one: O a. None of these O b. In|x +…

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Q: 2. Use Romberg integration to compute R3.3 for the following integrals. 0.75 (cos x) dx a. x In(x +…

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: 4. Calculate the following integrals a) S dx;u = x3 – 1 e 3x b) S - dx;u = e3x + 1 e3x+1 In x c) S*…

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

Q: Evaluate the integral in (7x) -dx. Choose the correct answer below. O A. - In (x) - 16 1 +C 16x* -In…

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

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