6. Evaluate the fallowing real integrals by residue theerem 3 2计 I = Ssine -d8;a>l anse 2(a- Ja?1)

Q: 14. Evaluate the integral: | ze dz. 1

A: Integrating by parts.

Q: Evaluate the indefinite integral: dz +C IV 36z2-1

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Q: 4 dr. 162? — 16х +13 Use the Table of Integrals in the back of your textbook to evaluate Perform the…

A: Indefinite Integration

Q: Evaluate the integral. * T/3 3 sec 0 tan 0 de In/4

A: Given that the integral is ∫π4π33secθtanθdθ. It is required to evaluate the given integral…

Q: 2. Use Cauchy's Integral formula, Evaluate the following sin42 IZ1= 3. (Z-4)3

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

Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral 8 x-6 So ²x+8 dx

A: Use fundamental theorem of calculus to evaluate the integral.

Q: Compute these integrals: dz 3114

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Calculate the definite integral of x^2 + 4x approaches from 1 to 3.

A:

Q: Calculate the exact value of each definite integral in Exer- cises 47-52 by using properties of…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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: How many integral solutions are there to the equation x+y=17 with x between 1 and 8 inclusive and y…

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Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫√(2x + 1…

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Q: 24 Use properties of integrals to evaluate S (2x – 1) dæ,if 3 11 24 S (2x – 1) dæ = 104, and f (2x –…

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Q: 2.x D' -8 .

A:

Q: 7 Evaluate the improper integral, if exists : dz (5 - 2)3

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Q: Compute the approximation  of the integral -4 to 4 e^(-x^2) using right endpoints with 4 rectangles;…

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Q: Find the indefinite integral

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Q: (3y- 2 )cy y´+2y+17

A: The given integral is ∫3y-2dyy2+2y+17. We have to evaluate the value of given indefinite…

Q: [(9)se x². d²+xdx + (x²-n²) y=0_ by substitution x== 1102 at 2 pt souhen Hence show that it has no…

A:

Q: u= 4-xneduce the ntegral to standand ferm Sonm dx 4-x)=

A: ∫x64-x72dx In this problem we need to reduce the given equation into standard form and solve the…

Q: dr 5. 2 ?+3 2

A:

Q: (i) Find the Cauchy principal value of the integral dr. +4z + 8

A: The objective is to find the Cauchy principal value of the integral ∫-∞∞xcosxx2+4x+8dx

Q: Consider the integral equation (1). With certainly it is fulfilled that H(s) equals: a,b,c,d

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Q: Evaluate the Integral / tanh (2x)đx. A @ --n|cosh(2x)| + C B -In|cosh(2x)| + C © 21n|cosh(2x)|+ C D…

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Q: 6 Use properties of integrals to evaluate S (3x + 2) dæ, if 9 S (3x + 2) dæ = 73. 5. 6

A: ∫abf(x)dx= −∫baf(x)dx

Q: .1 In x dx ха: -1

A:

Q: Find the indefinite integral (10tan?x+ 16)dx, а. 10tanx + бх + C 10 3 b. -tan'x+16x +C 3 10 3 tan'x…

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Q: 2 Write ftan² x sec⁹ xdx as a sum of integrals of odd powers of secant or cosecent. Start with the…

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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 given improper integral. Enter the exact value of the answer. 7 In(4x)dr 0,

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Q: Use reduction formulas to evaluate the integrals ∫ 8 cot4 t dt

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Q: 1. Use the Table of Integrals in the back of your textbook to evaluate ∫11dx/x^2√16x^2+36 a.Perform…

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Q: Use the form of the definition of the integral given in Theorem 4 in section 5.2 to evaluate the…

A: First integrate the function x2+7 with respect to x using the power rule of differentiation.

Q: Evaluate the integral from 0 to infinity of 1/[x2+5x+4] or show that it diverges

A:

Q: de 2/2 V5 9 18

A: Solution: Here let I=∫dxx29-x2 Substitute: x=3sinu u=sin-1x3 and dx=3cosudu Thus,…

Q: 4. Prove using the results concerning iterated integrals that In 5 dx = 4 sin? x

A: Given:-                 To prove the result concerning iterated integrals that…

Q: Compute the approximation  of the integral -4 to 4 e^(-x^2) using mid points with 4 rectangles, you…

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Q: Evaluate the indefinite integral. 4 V3+ adx + C

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Q: Calculate the indefinite integral 4dy V4-9y2

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Q: Use the Addition Property for integrals and the results of Section 5.2 to find values for r and s.…

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Q: Evaluate the integrals ∫√(25 - t2) dt

A: We have to evaluate the integral: ∫25-t2 dt Rewriting the integral, ∫25-t2 dt=∫52-t2 dt We know the…

Q: Evaluate the indefinite integral.

A: Consider the provided integral, ∫z21+z33dz Evaluate the indefinite integral.  Apply the substitution…

Q: Use Cauchy's Residue Theorem to compute the improper integral (x + 3) sin(x) dx (x2 + 1)(x² + 4)2 00…

A: Given that ∫-∞∞x+3 sinxx2+1x2+42dx Using Cauchy residue theorem, we can written it as ∫-∞∞z+3…

Q: 2 Evaluate the integral of x^3/square root (x^2+4) using a trig sub

A:

Q: 6. Evaluate the fallowing real integrals by residue theerem 3 do ans금 t cosG+ 2sing +3

A:

Q: Evaluate the integrals in ∫3 sec2 t/6 + 3tant dt

A: Given integral is, ∫3sec2t6+3tant dt

Q: You found that the reduction formula of a certain integral is In = 180 (13x" sin (13x) + næ"-1 cos…

A:

Q: Evaluate the integrals ∫8 sin4 y cos2 y dy

A: the given integral is: ∫8 sin4y cos2y dy we have to evaluate the given integral.   let the given…

Q: Suppose we perform the substitution .3 u=9-x in the integral

A: Given that:∫123x29-x3dx