Use the residue theorem to evaluate: o dx 0 x3+1 2n/3

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

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Q: Find the Taylor polynomials p4 and p5 centered at a = for f(x) = 10 cos (2x). 12 %3D P4 (x) =

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Q: Evaluate the integral | * elan(13-x) sec²(13 · x) dx 52 Write your answer in the form ea – b -

A: The given integral is ∫0π52etan13xsec213xdx. Let u=13x. Then du=13 dx. The lower limit will change…

Q: Find Taylor polynomial P, to f (x ) = 1 e* ;xo =1 , sin ax ;x0 Lnx

A: As per the instruction, we will answer only one question. Taylor series of function fx at a is…

Q: 6. Evaluate the following real integrals by residue theorem 3 or a>1 anso MTLWJ7 -bm 693 Cos mX ans:…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Use the substitution t = tan(x/2) to transform the integrand into a rational function of t and then…

A: Let  I = ∫0π2 5 sin 2x 2 + cos x   dx

Q: Find the Taylor polynomials pa and p5 centered at a = for f(x) = 5 cos (x). %3D P4(x) = D

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Q: Use the Fourier transform methods to evaluate the integral dx (r? +9)(x² +4)

A: In this question, we evaluate the integral by using Fourier transform. The integral is…

Q: Part (b) 5e Evaluate -dz by residue theorem, where C is the contour |z| = 2 6z4 +30z3

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Q: By using the Residue theorem, compute the integral eiz -dz, where I is the circle |2| = 3 traversed…

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Q: Evaluate the following improper integrals using Cauchy's Residue Theorem:(Convert them into a…

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Q: dx 2 -o x+4x+5

A: The general form of a complex number is given by , where a, b are two real numbers and . Any complex…

Q: Evaluate the improper intergal 1 dx using the residue (x2 + 9)* theorem.

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Q: Evaluate the integral f 2x (x2 + 5)" dx using the substitution 16 u = x + 5. 16 2x (x² + 5)" dx = +C

A: Solve integration

Q: Calculate the Tayorl Polynomials T2(x )and T3(x) centered at x=a for f(x) = 14 sinx, a=pi/2

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Q: Find the Taylor polynomials p1, .., P4 centered at a =0 for f(x) = 2 cos (2x). P1(x) =O %3D

A: Given : f(x) = 2 cos(2x) a point = 0 Onder = 4

Q: Find the area +6 C1 R -6 +6 C2: 4x2 + y² = 16 -6 using green's theorem.

A: We are given the above region of which we need to find the area and as per the instruction, we need…

Q: Va huate ble following Tuteprel using Residue theorem? dx 8 X1

A: Transforming the given integral into the contour integral of the form  ∫Cϕzdz=∫Cz2z4-1dz Where C…

Q: 5 dx 8x (x+1)? 1

A: First evaluate indefinate integral

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

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Q: Use the Fundamental Theorem of Calculus to evaluate the integral: 5/4 sin x dx. Jπ/2 C. A. - B. D.…

A: The objective of the question is evaluate definite integral using the fundamental theorem and choose…

Q: Find the product of the integral 1- S x²cos(xy)dxdy

A: We have to change order of integration first.

Q: Using the Cauchy residue theorem evaluate the following improper integral cos 2 dx (22 +1)2"

A: ∫0∞cosxx2+12dx=∫0∞cosxx+i2x-i2dx Let fx=cosxx+i2x-i2. Then f has singularities at x=±i with…

Q: Use the Residue theorem to evaluate the integral fe(z-2)dz.

A: Use the expansion of e1z  =1 + 1z + 12! z2 + 13! z3 + ...  Hence ∫e1z(z-2)dz = ∫(z-2)1 + 1z + 12! z2…

Q: Find the Taylor polynomials p1, .. P4 centered at a = 0 for f(x) = 3 cos (6x).

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Q: Use residue theory to calculate the following integrals: P.V. fo (a) P.V. 3x (x²+49) (x² - 2x + 5)…

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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: Find the residue f(z) = Z²-22 (2+1)² (2²44)

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Q: Find the Taylor polynomials p4 and p5 centered at a = 12 for f(x) = 8 cos (2x). ..... P4(x) = [ Ps…

A: First calculate the first 5 derivatives of f(x)…

Q: Use the Midpoint Rule to evaluate the integral fx-¹dx. Sx 1 O O O T N|W T 11133 113 21/3

A: Given integral is ∫12x−1dx. We have to evaluate the given integral by using midpoint rule. Here,…

Q: Find the integral:

A: Recall the formula:

Q: Evaluate the integral. cos(0) d0 Tt/2

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Q: Use Residue Theorem to evaluate each of the following integrals. de (a) 5-4 cos 0

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Q: Evaluate the integral f 2x (x2 +7)° dx using the substitution u = x² + 7. 2x (x? + 7)° dx +C

A: Solution:

Q: Apply Cauchy integral formulå to find the value of the integral: sinz Se dz; where C:|z| =. Also…

A: Note:- As per our guidelines, we can answer the first one as exactly one is not mentioned. Also, for…

Q: Find the Taylor polynomials p,- P. centered at a = 0 for f(x) = 3 cos (5x).

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Q: In (a le) (2- sec2x)m sec'x sec ( 3A – x) What should be the value of A for dr to be integrable…

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Q: Evaluate the integral. cos(6 z) dz %3D

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Q: Use symmetry to evaluate the followingintegrals.

A: The given equation is ∫-223x8-2dx The symmetric property for integral is expressed as…

Q: Find the Taylor polynomials p1, Pa centered at a = 0 for f(x) =2 cos (- 4x).

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Q: Use symmetry to evaluate the followingintegrals.

A: Given: ∫-22x9 dx

Q: Find the Maclaurin polynomial p3 for f(x) = cos( 중).

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Q: Evaluate the integral. sec3xdx A In sec3x+ tan3x+c There is no correct answer from the given…

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Q: x +1 x3 +1

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Q: Use the Residue Theorem to evaluate the a? integral dx + x2 where a>0

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Q: Use the residue theorem to evaluate: eix dx

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Q: Evaluate the integral. ƒ ƒ6(x³ - y³)²dA = □ (Type an exact answer.) R

A: ∫-11∫016x3-y32dA

Q: Use Cauchy's Residue Theorem, where appropriate, to evaluate the given integral along the indicated…

A: Given integral is ∮1(z-1)(z+6)2dz