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

Q: 3 Evaluate the integral c Ħ A) 1 B) 77 c) - Ť tan?xdx E)ユ-

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Q: H.W: Evaluate the integral (x²y - 2xy) dydx 1. 30 0-2

A: As per your query the solution of the question no 1 is given in the next step.

Q: 4. 1+(sin (20))2 6 cos (20)d0 4. 1+ (sin (20))2 6 cos (20)d0 a f(u) du where g(x) =u, to evaluate…

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Q: Express lim E=1 Ax ||PI0 as a definite integral where P is a partition of [0,2]. k%3D1

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Q: Evaluate the integral. ∫0pi 9sin^2(t)*cos^4(t) dt

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Q: 1 To evaluate the integral J dx, we substitute x = 3 tan 0-4. (z²+8z+25)*/2 Select one: O a. True O…

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Q: 4.3 Use the calculus of residues to evaluate the following integral r27 1 1+8 cos? 0

A: We find the given integral by using calculus of residues.

Q: Evaluate the indefinite integral. 2 (t) – 7e' + 8 + 1 + 12 2 sin(t) – 8 cos(t) + sec- dt = +C.

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Q: 4.3 Use the calculus of residues to evaluate the following integral r27 1 d0. 1+8 cos? 0

A: We find the given integral by using calculus of residues.

Q: Use the residue Theorem to show that T Cosh 7 2 sinh 7' 2 sinh² 7. 22 -1 -dz 3Di Se (22 + n²)² sin z…

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Q: Recall that 1, x >0 d (]xl) dx —1, х<0 x < d Use this result and the chain rule to find (sinx|) for…

A: Here, recall that  -π,-π2 is 3rd quadrant, where sin is -ve-π2,0 is 4th quadrant, where sin 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: Evaluate the following integral.

A: The given integral is,

Q: Evaluate the integral sin^4 e de from 0 to π/2 * 2π/3 TT/4 31/16 31/5 O h

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Q: 1) Evaluate the following iterated integral. 2/2 sin(2y) SS dydx y 0x

A: Use change of order of integration.

Q: Find the indefinite integral. | 15 7 19 – 14 d t8 - dt

A: Given: ∫t8 t9-149 dt Solve the integral. Method of solving: Substitution Method. Formula used: i)…

Q: 17. Use the theory of residue to evaluate the following definite integrals 2 de (2) / 2+ cos 0' cos…

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Q: If In y = 3 sinh x show that dy (a) (1+r2)()² = 9y², dx (b) (1+ x²)- dy da? dy +x- – 9y = 0. da…

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Q: 2 Evaluate the definite integral 16sin(t)cos (t) dt.

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Q: S-) Find the general soluhon of sin'x y"-(25inx.cos x)y'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Please check step 2 for solution

Q: 1. Evaluate the iterated integral: r12 Jo o cos(2) dy dx. -

A: To find ∫π2π∫0x21xcosyxdydx: First solve ∫0x21xcosyxdy: Let u=yx  dudy=1xdy=xdu…

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

A:

Q: Prove that for all r € [1, 00), – sinh (- |cosh-(x)|) = vVI² – 1.

A: We know that: Cosh-1x=logex+x2-1  and  Sinhx=ex-e-x2. And, Sinh-x=-Sinhx. Therefore,…

Q: Evaluate the integral: ∫cos^3(t/5)sin^2(t/5) dt

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Q: Evaluate the following real integrals by residue theorem 3 03 S <-1 X Sin mx X4 +1 OSH dx πT -m/√z…

A: As per the question we are given an improper integral from -∞ to +∞ and we have to evaluate it by…

Q: Gren thint sin (A+i6) = xtiy, 28 Prove that, 9父+ =1 snh'B 1) x essec?A -y' sec'A =1

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Q: (Find the integral curve of the following equation passing through the given point). y = 4 cos(x),…

A: Given dy/dx and point we have to find equation from this

Q: 4. Use residue theory to calculate the following integrals: 3.x (x2+49)(x² - 2x + 5) (a) P.V. (b)…

A: to solve integration we first find the residue of pole of the given function of upper half plane and…

Q: Evaluate the integral sin^4 e de from 0 to Tt/2 * T/4 O 2r/3 O 31/16 О З1/5

A: We have to evaluate the integral ∫0π2sin4θdθ. Use the reduction integral formula, which is given…

Q: 3. Use the IVT to prove that y = x ln x has at least one zero on 2'2

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Q: Evaluate the indefinite integral (7t)cos(10t) dt %3D + C

A: 2 cos(A)sin(B) = sin(A+B) - sin(A-B)

Q: 2. Find a closet rank-1 approximation in the f norm to A = cos 8 - sin e sin e cos 0

A: According to the given information it is required to find closet rank-1 approximation in the l2 norm…

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: Evaluate the integral of x cos 2x dx with limits form 0 to pi/2. (A) -3/4 B 0.75 C -0.5 D 1/2

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Q: In the case when U = x on the edge y = a (where Yo is a constant), a calculate C, inorder to show…

A: Given at y=a, U=ψ0ax     …Equation(1). And, on substitution of y=a in expression…

Q: -Jxcar (r<)= o x sin(ñ x) cos (Tx)

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Q: 1)the f a) 3 cosh z b) 0 c) in d) n -dz by using the residues is equal to

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Q: Evaluate the iterated integral. * T/6 cos(e) 7r5 sin(8) dr d0

A: Explanation of the answer is as follows

Q: Q:9 Evaluate cot(72)\dz 3 [z e? + by Cauchy's residue theorem.

A: We have to solve the given integral by Cauchy residue theorem

Q: separate the following into real and imaginary parts tanh(x+iy) sinh(x + iy) coth(x + iy)…

A: Given; i) tanh(x+iy) ii) sinh(x + iy) iii) coth(x + iy) iv) cosh(x+iy)

Q: 1. Evaluate the following integral: (6 + 3 cos x) dx a. Analytically b. single application of the…

A: In the Trapezoidal rule, we calculate the area under the curve by dividing the area into the smaller…

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: Evaluate the indefinite integral: 4t cos (t ) dt = %3D

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

A: Use the following formulae, to evaluate the given complex integral. Let z0 be a pole of order n,…

Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

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

A: Cauchy residue theorem is one of the method to evaluate the integral of analytic functions.…

Q: Evaluate the integral: ( ) sect tan ti +tcos 2t j+sin² 2t cos 2tk 1k)dt

A: the given integral is: ∫0π4sect tant i^ +t cos2t j^ +sin22t cos2t k^ dt we have to evaluate the…

Q: 2. Find the following indefinite integrals. (a) / sin(In(x)) xp (b) / º etan-(x) dx x2 + 1 sin(t)…

A: (a) ∫sinlnxxdx Let; lnx=t⇒1xdx=dt     =∫sint dt=cost+C put again: t=lnx =coslnx+C Result:…

Q: Let z=In(x²+y²) where x=ue"sin t and y = ue"cos t. If u=- 2 and 1=0 then is equal to %3D ....

A: Multivariable function: When a function f has more than one independent variable and only one…

Q: Determine the following convolutions by integration (a) 1 * sin wt (b) et * e

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