Q3: Evaluate the following integrals using Cauchy's residue theorem: where C: |z1/2| = 1. (z²+3z) dz 3) Sc 4) Je z³ cos dz where C:\z- 3/2| = 5/2. Z-2

Q: 6. Evaluate the following real integrals by residue theorem 3 • I = S ans: 2π (a-√a²1) I = J ∞ 27 2…

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

Q: 2. Find the following Integrals a) ſe (lnx)³/2dx 1 X 1 -1 tan-¹(x) dx 1+x² c) ſ sin³(x/2)dx b) √ ² ₁…

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Q: dt Use parseval's identity to prove that J a? +6²+?) 2ab (a + b) TC

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Q: A-Evaluat wing integrais: 1) S (cos x / sin? x) dx. 2) S (2x+4)/3 dx, use x-0 to x=2. 3)…

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Q: Q3) Use substitution to find the following integrals a. f sec²x √tan x dx b. dx x3 Sa (1+x4)5 C. csc…

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Q: prove that ਰ Apply the calculus of residues to dx (1 + x²)² - π 4 .

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Q: a) Let f(x) = 35 – 2a-1 +5+ 7x². Compute the integral of f. %3D

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Q: P2. Find the following Integrals (Inx) ³/2dx a) e x tan-¹(x) dx 1+x² sin³ (x/2) dx b) c) d) fsin³…

A: According to bartleby guidelines we do only first three subparts and rest part can be reposted .

Q: 16 Evaluate the integral f 2x (x2 + 7)º dx using the substitution u = x? + 7. %3D | 20 (2* + 7)" dz…

A: We need to evaluate the integral ∫2x(x2+7)16dx with the help of substitution. This can be evaluated…

Q: Consider the function f (x) = cos (2x) a) Find the polynomial of degree 4 centered at X = 1.…

A: The given function is fx=cos2x

Q: Q2) Evaluate the integral x* dx 0.

A: To evaluate the given integral

Q: Show that the form under the integral sign is exact in space and (3,9,0) evaluate the integral (2ay…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: We want to find Laplace inverse of given function.

Q: Use the calculus of residues to evaluate the improper integral COSX -dx. (x²+1)³

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