EX2 : Find Divergence and Curl of the field function f j = In (x? + y?)i – 2z -tan + (5z + e' cos z)k

Q: Determine weather the statement is true of false. Explain your answer.

A: Consider the given differential equation dydx=1x2+1 Use separation of the variable method to find…

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Q: 1. The following infinitesimals usually appear in integrals when we: ds dt AP dr dA da dx Df dr d:…

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

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Q: 4. Use the definition of the Riemann integral to evaluate f(x) dx where (a) f(x) = x². (b) f(x)= 3x…

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Q: 3 2(x²+1)7 Write down an integral that gives the ARCLENGTH of y on the interval from x = 0 to x = 2…

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Q: frt)dt is equal to Let f(x, y, z) = x-y+z and rt)=[sinh (t), cosh(f), where 0 sts1. The the integral

A: Formulae used: ∫sinh(x)dx=cosh(x)+C∫cosh(x)dx=sinh(x)+C∫xndx=xn+1n+1+C

Q: dx Evaluate the improper integral x(lnin x )²

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Q: :+cos(x2) dz. =(s* + 1) 4.1 with C: |z- il -. 4.2

A: Explanation of the answer is as follows

Q: dx Consider ·S= using rationalizing substitution. x1/2 + x2/3 Find the integrand in terms of z.

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Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by = - 2n…

A: The fourier integrals of two continuous fx and gx defined on ℝ are defined…

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: Find the Fourier integral of f(x) = e-k* when x>0 and f(-x) = f(x), hence prove that cos(wx) dw w…

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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: 00 1 (b) Calculate the improper integral dx , or show that it (x² + 25)3/2 -00 diverges . Show your…

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

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Q: 1. Prove that L{cos(at)} cos(at)dt integrating by parts twice and the evaluation of the improper…

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Q: Integrate f(z) = 6 tan(z²) counterclockwise around the unit circle, using Cauchy's integral theorem…

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Q: (0 if xE Q (1 if x E I If f (x) = show that f is not Reimann Integrable

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Q: Find the total differential of the following: 1. f(x, y,z) =-tan'(x + y +z)+ In(xyz)

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Q: Evaluate the integral (1+ sin t)' cos t dt using the substitution u = 1+ sin t. (1+ sin t)' cos t dt…

A: Recall: ∫xndx=xn+1n+1+C

Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by sintwa] 2л…

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Q: z'sin3z Evaluate dz with C: -2 using Cauchy's integral formula

A: *concept:- Cauchy Integral formula.

Q: I don't understant this hw problem

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Q: At the point of discontinuity on (0, co), the Fourier Cosine integral corverges to: f(x+) – f(x¯)]…

A: We have to solve given problem:

Q: | (t – cos(3t))e-'dt

A: Using definition of Laplace transform.

Q: Which of the following integrals determines the length of the curve defined by r(t) = 2ti + cos(t) j…

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Q: (a) Define the principal value integral from a to b of the function f(x), where f (x) has a…

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Q: What is the value of the line integral on the field 5xy? 5æ?y F(x, 3) = ()i+ ( 2 along any path from…

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Q: S Prove that £{cos(at)} = est cos(at)dt s² + a² integrating by parts twice and the evaluation of the…

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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: Compute the integral fo S x cos(xy)dxdy

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Q: The Fourier integrals of two continuous functions f (x) and g(x) defined on R are given by 00 f(x) =…

A: The Fourier integrals of two continuous functions fx and gx defined on R, where…

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: Evaluate the indefinite integral ∫⟨1t,4t3,√t⟩dt, where t&gt;0.

A: We will integrate term by term.

Q: What is the value of the line integral on the field 5a² y F(x, y) = () i + 5æy? 2 2 along any path…

A: The given field is Fx,y=5xy22i→+5x2y2j→. Consider the function fx,y=54x2y2. Now,…

Q: Evaluate the integral. "π/4 J.T tan (0) sec²(0) de

A: This question can be solved using integration by substitution.

Q: Q3: Evaluate the integral f xe dx by first finding the Maclaurin approximation to the integrand with…

A: The Maclaurin series: fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+… Where centered at a=0 or x=0. Given:…

Q: rea bounded by the small loop of the limaçon r 1 2 sin e is given by finite integral

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Q: Transform Bessel's equation x²²y + xdx+(x²-n²) y=0 by substitution x== souber moitops navig Hence…

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Q: i +j- t3/2 k ) dt |

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Q: use Greens Theorem to evaluate . cosy dx + (xy- x siny)dy Ewhere C is the bounday of the y Jx,…

A: We have to evaluate given integral using Green's theorem.

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: xcosr (i) Find the Cauchy principal value of the integral dr. ² + 4x + 8

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: 8. Find the area under the curve of f(t) = 1.2e0.1t betweent=1 and t = 2. %3D

A: From the given statement, the function

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: Evaluate the integral: f/2² sin (-) dt du ,2

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Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

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Q: gral can be parametrized using Feynman inte -x cos(tx) dx, where t = 4, and I(0) = e dx = 0. ming…

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