By integration find the Fourier transform of Ax)=2r+1 _if þx|<1_and fx)=0 otherwise.

Q: Find the fourier expansion for the function whose definition - - <x <- 2 x, - 2 (x) 0, <x< 2 2

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Q: use direct Fourier transform formula to prove thès 8o -at t é ut ult)

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Q: What should be the rewrite of the integrand of * (2 x + 5)² so that the resulting integral is…

A: SOLUTION-

Q: Find inverse Z-transform 1+- X(z) = (1 - -)*

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Q: Use (3) from Section 5.4 to evaluate the integral. In 9 ex dx =

A: Integration of e^x is itself

Q: Use the substitution formula to evaluate the integral. 2t dt -1

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Q: Find the orthogonal trajectories of the family of curv

A: In this question we will use basic of calculus i.e concept of orthogonal trajectory. We will simply…

Q: 8(x – a) + 8(x + a)

A: Topic:- calculus

Q: Evaluate the integral. 4 (5 - t)Vt dt

A: The objective of the question is evaluate the definite integral.

Q: Evaluate the definite integral exactly, using the Fundamental Theorem. 6. 1 -dt 1 dt II

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Q: 2. Use the fundamental theorem of calculus part 2 to compute the integral 1° dr. 0,

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Q: 2dy Зу-4

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Q: Express f(x) by the Fourier integral where f(x) = - 2, -3< * < 3 otherwise. %3D

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Q: use convoluHon Lapiace transform 15. to find Inverce (1+zs) =S

A: Let ft &amp; gt be functions with Laplace transforms Fs &amp; Gs respectively that is Lft=FS &amp;…

Q: Integrate from 0 to 2

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Q: Use the results of Section 5.2 to compute the following definite integral: 3x² dx

A: We need to evaluate the following integral ∫-453x2dx Formula Used : ∫abxndx = 1n+1bn+1-1n+1an+1

Q: Show that is integrable on [0, 1]. f(x) = {1. 0, +√√xsin(1/x6), x‡0 X 0

A: Given that f(x) = 1 + x sin 1x6,x≠00,x=0 To prove that, f(x) is integrable on [0, 1]

Q: Find the indefinite integral: O 10sin 3x - 20 cos 2x +6 e5x + C 90sin 3x 60 cos 2x + 150 e5x + C…

A: The objective is to find the indefinite integral.

Q: 4. Express f(x) by the Fourier integral where f(x)= (-2, -3< x < 3 otherwise.

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Q: Use a Fourier cosine expansion to solve

A: Since I have solved similar problems, let us solve the given question step by step ... By using…

Q: 1 point) Evaluate the definite integral. | * In(2t)dt

A: We will do integration by parts.

Q: Perform a test to determine if it converge or diverge -1 x 2sin 1 dx 1– x -1

A: The function is given by: ∫-112sin-1x1-xdx If the function fx=2sin-1x1-x is positive, continuous and…

Q: From the Fourier expansion of f(x) = la- x) (x(1+x) -1<x<0 V. show that

A: Solution

Q: Solve: The integrand (1-cos2 4t) cos4t dt on the integral 0 to pi/12

A: Use Pythagorean identity. 1-cos^2 theta = sin^2 thetahere theta= 4t

Q: Evaluate the integral in terms of Beta function: , (1- a)'dr (SAN) OP(4, 2) OP(1, 4) OP(8,4) OP3,4)

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Q: Compute this integral ∫ (xsin^2(x)cosx) dx

A: We use integration by parts

Q: Solve for DE: separable DE

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Q: Evaluate the integral. VZ/2 dr V1-2

A: In this question we have to evaluate the Integral.

Q: Evaluate the integrals ∫et cos (3et - 2) dt

A: We have to evaluate the integral: ∫et cos3et-2dt In this case we should use substitution method…

Q: Use (3) from Section 5.4 to evaluate the integral. In 2 ex dx = /1

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Q: Use the results of Section 5.2 to compute the following definite integral: 4x2 dx %3D

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Q: Show that A and AT have the same nonzero singular values. How are their singular value…

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Q: The integral expression J 2x sec( 5x) tan (5x) dx can be evaluated using integration by parts of the…

A: Given that: ∫2xsec(5x)tan(5x)dx

Q: Find the Fourier integral foxx) 5 if -25X TO -8 iP xx2

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Q: Evaluate the integral. 4 sec2(2t) dt 3+2 tan (2t) 2 4 sec (2t) dt%3D 3+ 2 tan (2t)

A: See the details solution in below

Q: Only piecewise continuous functions f(x) on every finite interval (0, ∞) such that F(x)| dxis…

A: The given statement is false.

Q: The double integral; ) dA Sin(x2+y², (4+X2+42)- 2. is it convergert this regon; Conu in {x20,y>OS

A: Now, we need to verify the convergence of the above integral.

Q: fer) sen ax %3D

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Q: Evaluate the integral. dt 4 dt =

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Q: The Fourier integral of (-1, -14 < x < 0 1, 0<x< 14 0, otherwise f(x) = {

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Q: How do you integrate z/(z+2) in terms of z?

A: Here, integral is,

Q: 8. S(1- sec3x)²dx

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Q: The integral expression 2x sec(5x) tan (5x) dx can be evaluated using integration by parts of the…

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Q: Compute the integral S do 2-sin 0 *

A: Apply linearity: Apply tangent half-angle substitution:

Q: section method to

A: Given,         f(x)=x-cos(x);     0, π

Q: Only piecewise continuous functionsf (x) on every finite interval (0, 0) such that 00 | S(x)| dxis…

A: According to the condition of convergence for Fourier integral,  Let f and f' be piecewise…

Q: Use (3) from Section 5.4 to evaluate the integral. In 6 e* dx =

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Q: sec² (1+ /7) dr. 6) Use the substitution u = 1+Va to evaluate the indefinite integral|

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