[4] 5. Use the fact that 1 +C 4e2r dx = 2e2 to either evaluate the improper integral 2 dr, or show that it diverges. 2r

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A: Value of the giveen integral is

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Q: 2. Suppose | 29(r)dr = 10. Using linearity properties of integrals, calculate | (g(x) + 3)dx. 3

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A: as per our guidelines, I am solving only the first question with both parts please resubmit other…

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A:

Q: Evaluate the integral. ( 3ett - 12e2t + 4 14) e2t + 4 dt r (x +5)2 tan-1(2x) + 4x3 + x 15) dx (4y2…

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Q: 12. Evaluate the following integrals. a. S (9t+ 415) dt b. Se-4* dx **3** dx d. f(x-1- x + 4t3…

A: Note: Since you have posted multiple sub-parts we will solve only first three for you. If you want…

Q: 3. Decide if the following improper integrals converge or diverge. dx (a) x2 + 4 (b) xe" dr da (c)…

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Q: express L−1[F(s)G(s)] in terms of a convolution integral.

A:

Q: 9. Evaluate the integral // V2 + y² + z² – 3 dV where S lies between a² + y² +2² = 1 and a? + y² +…

A: Given integral, ∭sx2+y2+z2-3dV Where S lies between x2+y2+z2=1 and x2+y2+z2=9. The spherical…

Q: Just use the definition L{f (t)} = ° e-st f (t) dt with 2 integrals, one for 0 1

A: Laplace transferom

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: Express the general solution of dy/dx = 1+ 2xy in terms of the error function erf(4) = dt.

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Q: 00 1 (b) Calculate the improper integral dx , or show that it (x² + 25)3/2 -00 diverges . Show your…

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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&gt;1

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A: Differential equations

Q: Find the complimentary function and particular integral for (D² – 5D+6)y = e2x cos(2x).

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Q: The improper integral J dx converges to x-5 4 о попе 1

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Q: S B+1F dx (Improper Integral) (3x+1)?

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Q: So S(x + 3) dy dx 3. Evaluate the double integral:

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Q: -2 2x Jo x2-4 Só dx (Improper Integral)

A: Let I is the value of given Integral.

Q: Q1/Evaluate the integral: -За (2Vах dy dx x2 0, 4a by changing the order of integration.

A: We have to solve given problem:

Q: : Evaluate the double integral : (x + 2y – 7) dy dx 00

A: The solution of double integral is 126

Q: 4. S dy y³-2y²

A:

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.…

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Q: 1- xy dy = 0. 1+ xy

A: 1+xyx2y.dx+1-xyxy2.dy=0 (Now multiply both sides by (x2y2) ): y1+xy.dx+x1-xy.dy=0 or,…

Q: •1 r1 Evaluate the double integral / /. cos(y*) Vy³dydx

A:

Q: Q1 (a) Compute the multiple integrals of (i) V4-22 xy dxdydz (11) S, (8 – x² – y²)dA, where R =…

A: In this question we will use basic of calculus i.e concept of multiple integration. We will simply…

Q: 2. Evaluate the integral 8- (a) L« (4t5/2 – 3t3/2) dt (d) 2 - Vt dt r4 (e) t2 cos e de JT/4

A: The objective is to find the values of given integrals

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Q: Q4 Evaluate the double integrals: ||x+y+1)dxdy

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Q: Find the value of the improper integral or state that it is divergent. (If it is divergent, enter…

A: We will calculate the definite integral using basic definite integral properties and if we get an…

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Q: 3 x2 Calculate the integral: dx V5 + a?

A: Given,          ∫3x25+x2dx

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: 1. Compute the given integral. Using Substitution Method 5x-12 dx = +C 5x2-24x-1 *

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Q: Q.1) Evaluate the following integral ez dx (2e2 – 4e* – 1) - -

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

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Q: 6. How would you begin to numerically approximate the double integral: bd 1-SSS(x.y)dxdy ac

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Q: Evaluate the Double Integral. 4 V16-x2 b. 2x dy dx

A: We have to evaluate

Q: 2t + 1 What is the indefinite integral of dt ? t3 -8t + 21t – 18

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Q: 2t + 1 What is the indefinite integral of dt t3 -8t + 21t – 18

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Q: 1 dx. 10. Evaluate the improper integral m 64 + z²

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Q: 2. Evaluate the following Integral by using suitable method: 2y3 + y y4 + y2 + 1 dy -

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Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate: