Substitute u = x + 2 into u10 - zu° +c to evaluate the given integral in terms of x. 10 x(x + 2)8 dx =

Q: Find Particular integral (P.I) (D² -1)y =18

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Q: Evaluate the integral. (e* i + 4t j + In(4t) k ) dt + C

A: The given integral is: ∫et i+4t3 j+ln(4t) k dt

Q: Substitute u = x + 2 into ul0 - 2u° + C to evaluate the given integral in terms of x. 10 | x(x + 2)8…

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Q: subpart D

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Q: 1 Suppose we perform the substitution u=3+Vx in the integral dx . I (3+ Vx)4 What is the resulting…

A: we have to find the given integral

Q: Evaluate the Integral dz 1. S z²+4z ANSWER: 1. - In + C 4 |z+4

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Q: T 3. fz sin4 y cos7 y dy 2

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Q: 8x Evaluate the given integral Jo (4+x²)2 dx using the substitution u = 4 + x². A. Estimate to three…

A: topic - definite integration

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

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Q: Evaluate the integrals in Exercises 1. esin (e) dx 2. e cos (3e – 2) dt

A: Given the integration I=∫exsin(ex)dx

Q: For 1/2 U -dx and using the substitution -du -du 4u √4-(2u²) ² 4u du -du 1/2, the resulting integral…

A: In this question, we want to know the Integral form after substitution.

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

Q: Evaluate the iterated integral. e² (1/xz In(z) dy dz dx

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

Q: 2. Evaluate the integral using FTC Part 2. d e²-t st². t dt dx

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Q: For x 1/2 dx and using the substitution u=x1/2, the resulting integral takes the form: 4u -du 4-12…

A: We can solve the integral by using substitution .

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: Evaluate the integral p.v. J e2ix -dx. 00 x+1

A: We can apply Cauchy integral theroem to find the integral.

Q: 2. Evaluate the given integral. a da /3 — а 0,

A: Given:                 ∫02a3-αdα Apply u-substitution: u=3-α⇒du=-123-a…

Q: We'll now apply the integration by parts procedure to the new integral e70 cos(80) d0, letting U =…

A: The given integral,∫e7θ cos(8θ) dθ

Q: In evaluating z(4– æ)šdx,if we use the substitution that u = 4 – x, then what will be the resulting…

A: Given that, The integral is following, I=∫x(4-x)13dx If we substitute,   u = 4 - x, the what will be…

Q: Consider the indefinite integral Jet +* dx: 5x+4 a) This can be transformed into a basic integral by…

A: Given query is to find the value of integral.

Q: Evaluate the following integrals. [e² sec ³ (eª) da 1 2 6 tan¹ x dx I 3 4 √9-w² w² dw pln(4/3) et dt…

A: Given data:- ∫x2dxx2-152, x>1

Q: dx e2a +5

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Q: S- For x 1/2 U 4u U dx and using the substitution -du -du -du 4u 4- (21²) ² -du u=x1/2, the…

A: The objective is to find the correct option.

Q: The improper integral (A) e B) © ⒸO D 1 8 Stoe ex dx is

A: Given that,

Q: a) Consider the following. 5x dx (x²+1) i) Find z = (In t)² dt ii) Evaluate the integral

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Q: Evaluate the integral (t³ In ti+ 3t³ sin (t) j+k) dt.

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Q: Find the approximations   T 8  and    M 8    for the integral integral 0 to 1 cos (x 2   ) dx

A: Given ∫01cos(x2)dx

Q: The particular integral of (D² +1)y = x is

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Q: Compute the following integrals. 1 t3 (a) dt. Jo V4+ t² (b) e6x cos (3e2) dx. (Hint: you might need…

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Q: Which of these is a non-elementary integral?" ( In(2y² + 1) -dy 4y A. * cosh(2x) xp. B. +…

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

Q: Evaluate the integral ez+1 dz a) 0 eZ+z

A: Given Data: Integrand: ∫01ez+1ez+zdz Let u=ez+z, The derivative of u with respect to z is,…

Q: Q/5 Evaluate the integral of: (a) St³et* dt dx (b) 2 x (In x)²

A: We have to evaluate the integral. Using the substitution method we can solve these questions.…

Q: In evaluating z(4– 2)šdx,if we use the substitution that u = 4– 2, then what will be the resulting…

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Q: In evaluating | x(4 – x)3dx , if we use the substitution that u = 4 – x, then what will be the…

A: Indefinite Integration using substitution

Q: B)Evaluate the integrals: i) S ii) f/2/2 x 2² siny dz dy dx. rdrde,

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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: Evaluate the integrals below. -4 x²+6 а. 1 Vx t/7 b. sin(t) dt It/3 c. Sx2Vx3 + 2 dx

A: a.=∫14x2+6xdx=∫14(x2-12+6x-12)dx=∫14(x32+6x-12)dxintegrating=[x32+132+1+6x-12+1-12+1]14…

Q: dx S. 2x - 1 e

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Q: Calculate the following integral: 4 I V16 - x dx .2 0.

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Q: 2_ Calculate the generalized integral. x In r dx J. (1+12)3

A: The given integral: Calculate the above integral:

Q: In evaluating x(4 – x)3 dx , if we use the substitution that u = 4– x, then what will be the…

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Q: Find the integral of t/(t^4+2) dt

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Q: The result of the integral in 0 given |V y²– 25 -dy is 5 tane – 50 +C, y (A) True (B) False

A: To solve the following integral

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) YV 6 +…

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Q: find the integral from 1 to 4 of (3t^(3/2) i+(t+4)(√t)k)dt

A: The given expression is ∫143t32i+t+4tkdt. Evaluate the value of integral. Here we use the formula…

Q: Match the correct representation of "u" to evaluate the given integrals by the method of…

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Q: Evaluate the integral of ax^2 e^bx dx assume a and b are constants.

A: Please see the explanation below

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.