00 cos wx Q1/ Use Fourier Integral to show that 0. dw w2+1

Q: Evaluate the integral: integral fom 0 to pi/2 sin^2 x cos^2 xdx

A:

Q: 5. Verify Green's Theorem for 0(xy +x )dx+(4x-1) dy where Cis shown below by (a) computing the line…

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Q: TC 16. Evaluate the definite integral cos2 (4t –) dt

A: 16. Now,

Q: Evaluate iterated integral.

A: ∫03∫45xx2+3ydydx

Q: (cos v)³ + sin v dv (cos v)²

A: The given integral is: ∫cosv3+sinvcosv2dv Let I=∫cosv3+sinvcosv2dv

Q: Evaluate the double integral sin(y' +1)dydx.

A: Use the change of order of integration to solve this problem.

Q: Calculate the iterated integral. dx

A: Value of the integral is (9/2)ln2  See below the explanation

Q: Evaluate the integrals: V2 1- dx (T/2 7cost sin t dt 2-

A: as per our guidelines, I am solving only the first question with both parts please resubmit other…

Q: 5. Calculate the double integral f, sin(2x) cos(3y) dA , R = [0, 1/2] x [0, 1]

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Q: Evaluate the integral. cos y dy sin 2y + 2 sin y – 3

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Q: Use Green's Theorem to evaluate the line integral. ex cos(2y) dx – 2ex sin(2y) dy C: x2 + y2 = a²

A: Use Green's theorem

Q: Evaluate iterated integral.

A: Given, ∫01 ∫36 xx2+3y dx dy

Q: T/3 3 sin (3t) -dt. 5 - cos (3t) Evaluate the integral

A:

Q: ) Evaluate (3t+ 5) cos dt using integration by parts. 4.

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Q: Find the indefinite integral. |cos 2x ein 2* de sin 2x A) 2 +C ein 2x +C B) C) sin 2x e cos2x +C D)…

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Q: Calculate the integral (а) dx (*/3 Vtan 0 (b) п/4 -do sin 20

A: Given : (a)  ∫-∞∞x5e-x2 dx    (b) ∫π4π3tanθsin2θdθ

Q: -Find Fourier Integral for the function: f(x) = {0 x 0 0 <x < 2 1 ans: f(x) = - " sin2w cos(wx) +…

A: Given function fx=0    x&lt;0 or x&gt;01    0&lt;x&lt;2 So we must have  fx=0    x&lt;0 or x&gt;21…

Q: dx so that the resulting integral is integrable? What should be the rewrite of the integrand of…

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Q: Evaluate the integral: S/2 sin(4t - u) du dt

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Q: Estimate the error if cos Vt is approximated by 1 – in the integral , cos Vi dt. 4! 6!

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Q: Calculate the iterated integral. 2 (6 7e* + 3y dx dy

A: From the given problem: I=∫02∫067ex+3ydxdy So, we can also write as: I=∫02∫067ex·e3ydxdy

Q: 5e* dx d. J J1-e2x 1+cos (2x) е. sin2 (2x)

A: Using the substitution method and solve the integration explanation is given below...

Q: Evaluate the following line integrals in the complex plane by direct integration (not using…

A: Complex

Q: Calculate the double integral. 7x sin(x + y) da, R = [0, * [0, =]

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Q: Compute this improper integral showing all steps.  integral of x ln(x) dx from 0 to 2.

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Q: Compute the definite integral T/4 0 5 sin² (3x) dx

A: Sol:- ∫0π45sin23xdxTake the constant out:  ∫a·fxdx=a·∫fxdx=5·∫0π4sin23xdx=5·∫0π4121-cos6xdxTake the…

Q: Calculate the iterated integral. 12 2ex + 3y dx dy

A: Consider the inner integral, name it as I1 Take the constant 2 out of the integral sign.

Q: Calculate the iterated integral x² ,3 sin x dy dx.

A:

Q: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the 10 cos t, y in (0 <t: curve C: x =…

A: A detailed solution is given below.

Q: Sin (x-t) u(t) dt = 1- Cos x

A:

Q: Evaluate the iterated integral. (3x - 2y) dy dx 1 Jo

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Q: п/2 (siny 1. dxdy 1-х2

A: We have to solve the integration

Q: Calculate the iterated integral.

A: To calculate the iterated integral ∫05∫142xy4+3dydx

Q: Evaluate the integral. * T/2 sin³x cos y dx

A: Using identity         Sin2x+cos2x=1

Q: Evaluate the integral / cos (r) sin(x) dx 16 COS using the substitution u = cos(x). ,16 cos" (x)…

A: This question is based on indefinite integral.

Q: Consider the following. dz 4z + 2 1 Find a substitution to rewrite the integrand as du. 4u du = dz

A: Given : ∫dz4z + 2

Q: Use Green's Theorem to evaluate the line integral. et cos(2y) dx 2ex sin(2y) dy C: x2 + y2 = a?

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Q: Integrate f(z) = 1 counterclockwise around the unit circle, using 28 – 4.4 Cauchy's integral theorem…

A:

Q: evaluate the Cauchy principal value of the given improper integral. cos 2r dx x² + 1

A: We have to find the Cauchy principal value of the improper integral. First we have to write the…

Q: -1 sinx dx %3D

A: ∫01/2arcsin(x) dxIntgerate by parts ∫fg=fg=∫f'gf=arcsin(x),…

Q: 1. Evaluate the trigonometric integral. (1) [20sin² (2x)cos (2x)dx (ii) S4ta dt

A: Given integral is: I=∫20sin22xcos22xdx To solve this integral we will use the following…

Q: Evaluate the double integral: cos(y') Vy3 dy dx.

A: The solution is given as

Q: Find the general indefinite integral using definition. (3t*-t³+6t²\ a) dt b) S(3 sin x – 4e* + 5* +…

A: Part a,Given,          ∫3t4-t3+6t2t4dt

Q: What is the Laplace transform of the convolution integral of h (t) = sinh 3t u (t), x (t) = cosh(3t)…

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Q: Give the general antiderivative for the integrand in the definite integral (cos +1)dx. cos x

A: Simply integrate and put the limit than simplify.

Q: Find the total differential. z = e4x sin(3y) dz =

A:

Q: Evaluate Poisson Integral: In(1-2a cos(x) + a²) dx ,a.) [a| 1,

A: To evaluate Poisson's integral: ∫0πln1-2αcos(x)+α2dx  a)α&lt;1 b)α&gt;1

Q: 1. Evaluate the iterated integrals. √27x² (a) [sin - dydx (b) √√x² - y² dydx

A: