6. Evaluate the fallowing real integrals by residue theerem ? dX ニ ans : こ。(X+a?)2 493 • I- ans B 12 (btx)いx)

Q: Use symmetry to evaluate the following integral. 2 ja (2- |x|) dx - 2

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Q: 2Sin Cze) 4-COS S (zt)

A: The solution for the above question is as shown below.

Q: Compute the Cauchy principal value of the following integral using residue theory details): 2+1 dz…

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Q: G.. Evaluate the fallowing real integrals by residue. theerem 3 -bm e 응) co3 mx (x4a?) Cx+b?)

A: This is complex analysis problem, we apply the residue theorem to solve the problem.

Q: Evaluate the indefinite integral. 4 dt (t + 11)? + C

A: Integration of 4/(t+11)^2.

Q: Evaluate the integral 5a2 - x+27 da. (x2 +9) 5x3 x2 + 27z) · In|r(x² + 9)|+ C 2 3 In |피 + 2z In |2…

A: Topic - indefinite integration  Note- as per our guideline if more than one question uploaded only…

Q: tan (In |4x2|) -dx is b in cos (In |(2x)*|)|+c. The integral of What is b?

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Q: Evaluate the indefinite integral. asin (a)cos(2)dz: + C %3D

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Q: The improper integral da is given by: Az-5 Select one: sec((b-2)/3) O a. 1 lim 3b 100 soc(4/3) Csc 0…

A: The given proper integral is;  I=∫6∞1x2-4x-5dx

Q: Use a substitution of the form u = ax +b to evaluate the indefinite integral belov 7x+1 dx 7x+1 dx%=

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Q: Consider the indefinite integral r523 + 2х? — 72х-32 2x2 – 72x dx 16 - Then the integrand decomposes…

A: Evaluate definite integral ∫5x3+2x2-72x-32x2-16dx

Q: 2x Evaluate the improper integral dæ, if it exists. (x2 + 64)2

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Q: What change of variables is suggested by an integral containing * Vx² – 4? O a cosø O none of the…

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Q: 2. Use the Definition of Residue to show that: dz -ni Izl=1 z² sinh z 3 Where 0 < |z| < T.

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Q: Evaluate the integral. ∫0 π/4 tan4 t dt

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Q: 6. Evaluate the following real integrals by residue theorem 3 T 211 I- -S do coso + 2 sing +3 ans o…

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Q: Evaluate the definite integral (from 5 to 7)∫(d/dt (2+2t^4)^(1/2) dt using the Fundamental Theorem…

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Q: Compute the double integral nx' ydA over the domain D indicated as 0 < x < 3, x < y < 4x +2. (Use…

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Q: To evaluate the integral / V2x² – 4dx,we may substitute x = 2 sec 0. Select one: a. None of these b.…

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Q: 4. Use residue theory to calculate the following integrals: 3x (a) P.V. · Loo (2²+49) (2² - 2x + 5)²…

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Q: Identify the type of generalized integral +00 fx'e* dx- and in continuity (if converging) to be…

A: According to question,Given Integral,Let I= ∫0+∞ x2ex3 dx

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫ cos (2x +…

A: ∫cos2x+5 dx Now put 2x+5=u Differentiating with respect to x, we get 21+0=dudx⇒2 dx=du⇒dx=du2

Q: 21. Write the definite integral that repre formed by y = x² + 2x + 1 and y=2x+5. Do:

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Q: Make the given substitution to evaluate the indefinite integral. 28r dr .u= 3-r 3-r'

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Q: 6. Evaluate the following real integrals by residue theorem 3 ーン ans : 493 • I= ST dX ans 8 12…

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Q: tan (in |4x2|) dx is bin sec (In |(2x)ªl)| + C. what is ba The integral of A B) 4 © 1 1

A: Topic:- integration

Q: Consider the following propositions associated with the study of the +∞ dx J - 1.1² √6 +1 improper…

A: Given : ∫1+∞dxx  in which 1x6+1≥1x

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where u> |z| > 0

A: Prove,∫z=1dzz2 sinh z=-πi3 ∫z=1dzz2 sinh z=∫z=1fz dz .........equation 1 fz=1z2 sinh z , 0&lt;z&lt;π…

Q: Use the substitution. 9 tan(0) to evaluate the indefinite integral 85dx +C J z²Væ² + 81

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Q: tan (In |4x²|) dx is bin sec (In |(2x)^)| + C. what is b? The integral of (A 4 1 B c) 2 1 D 2

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Q: 2. Evaluate the indefinite integrals: D = tan r secʻ r dr 8x + 7 dr 72 +1 E = - 2dr F = dr V9 - 36x2

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Q: Compute the following integrals using Residue Theorem. 52 - 2 a. b. dz 232-27 4² dz Soz (z − 2)4 dz,…

A: To compute the given integrals using Residue theorem. Residue theorem: Suppose f(x) is analytic in…

Q: -dr evaluate the integrals by substitution method J 2dx V2+r /2+x

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Q: Find the indefinite integral.

A: Given : ∫tan2tt2dt

Q: Evaluate the integral Ja (2 – 4)°dæ (x³ – by making the substitution u = x° – 4.

A: Consider the given integral

Q: Evaluate the definite integral. •4 ti + t?j| dt 3 |(7 - 1) 2 17 3 173 3

A: The value of the given integral is 1/3(173/2 - 1)

Q: 6. Evaluate the fallowing real integrals by residue. theerem 3 -bm -am 응) Co3 mX ans : X Sin mx ans…

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Q: 6. Compute the following integrals using Residue Theorem. 5z - 2 a. dz S dz b. So 22(2-1)" z(z-2)4…

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Q: Evaluate the definite integral. L, 3r/16 - z'dr 3x/16-2dr

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Q: Show detailed solution for the following integral: (Non-anonymous questionO) S tan'z sec³z dz 7

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Q: Use residue theory to calculate the following integrals: 3x 1. Loo (x² + 49) (x² − 2x+5) (a) P.V. dx

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 4. Evaluate the integral. (a) (2r-4r + VE) dz + 4x) dr

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Q: Evaluate the integral. I sec (8x) dr tan(8z) In(cos)(3r) 64 +C X

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Q: What is the integral of f 2z²–3z+2 1 -dx? O vi tan () +C 7 O None of the choices Gan '(녹루) + C 4z 3…

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Q: The result of the following double integral is 2 2 у ST (6 x² y - 5 e)dxdy= ? 0. -2 y 909 -20e? +…

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Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: Given, ∫0π42cos(x)dx

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

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Q: Evaluate the integral dz dy dr. -2 Jo 5-722-7y2 32

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Q: Choose the most appropriate answer: Evaluate the integral : f 7x6 dx x7+2 O In(x7+2) + C O In(x7+ 2)…

A: We will use substitution method to solve the integral.

Q: ydy +4y+11

A: