(2) Using Fourier transforms, solve the integral equation for f(x), 1 1 -a|x| - e- -b|x| = L / e-blul f (x - u)du, b 1 -e a where a and b are positive parameters.

Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

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Q: Using Fourier transform, solve the integral equation for the function f. r²e=" if r20 h(r) = f(r –…

A: As per the question we are given an integral equation in terms of a convolution between f(x) and e-x…

Q: (a) F{e-al a > 0.

A: Consider the following

Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 n = 4 (-x¹ + 22x³ -…

A: (a)How large should n be to guarantee that the Trapezoidal Rule approximation  to is accurate to…

Q: (4)Evaluate the definite integral (a)(1+ si 0 1+ sin x)dx (b) (2t+cost) di (b) f( -x/2 x+ X - dx R/4…

A: Explanation of the answer is as follows

Q: d Prove that x" Jn (x)] = x" Jn – 1 (x) %3D dx

A: prove

Q: Let f(x) = x/x), (0<x<10) then Fourier coefficient a20 has value when an even periodic extension is…

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Q: [6] Find the Fourier integral representation of f(x) = { 02 0 1.

A: Fourier integral representation

Q: of degree 2 )dx is equal

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Q: 235 óf the textbc (d) F{e* ,5iz-az²

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Q: Find the Fourier integral representation of the function, "a²-x² if 0a f(x) =

A: Given that  fx =a2-x2if  0 &lt; x &lt; a0if   x &gt; a The Fourier integral of f(x) is given by…

Q: (b) Find the Fourier integral of the function f(x)=e** when x>0 and f(-x) = -f(x) for k>0 sin and…

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Q: Fourier cosine integral (a) representations : =x² + a² if 0a.

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Q: Derive the numerical integration for Boole's Rule given by b- a | f(x)dx= l4(f) = [f(a) + 32f(x1)+…

A: Substitute n=4 in the general formula for solving numerical integration to obtain the expression of…

Q: (ex, if 0 a 3 Represent the function f(x) = { as Fourier cosine integral.

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Q: Evaluate the integral (i) S(tan xtan(2 – x) – tan (2 – x)tanx) dx (ii) Se*tan-'xdx -3 1 (iii) dx -3…

A: According to our policy, only 3 questions will be answered. For the remaining question, please…

Q: the integral of (15tan-1(x))/x2

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Q: ind and classify the Singularities of the function Z f(z) = @= (2-1) Sin the ZeroS -

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Q: Find the Fourier integral representation of the function f(x) = {1x1₁ |x T

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Q: 50, dex(+) = -25 (+ + 2) + 25 (1-0) + 15 (t-1) at 2 = -√(x + 2) + 251f) + 5lt-2) By using…

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Q: Find the Fourier integral of the function f(x)= e* when x> 0 and f(-x) = f(x) for k > 0 cosix and…

A: Fourier integral, for even function

Q: We will try to compute the real integrale-1²/²e-itz dr. Let R> 0 and let y be the rectangle with…

A: As per the question we are given an improper Integral whose value we have to find by finding : The…

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

A: The given statement is false.

Q: f(x) = (sinx if 0 π

A: This is a question of Fourier Analysis.

Q: Consider the function f(x) = cos(2x) for -2pi &lt; x ≤ 2pi and zero otherwise.A) Show that it meets…

A: A) Condition for Fourier Transform To have a Fourier transform, a function must be absolutely…

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

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Q: Orthogonal Properties of Legendre's Polynomials: L, Pm (x) P(x) dx 2 2n +1

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Q: Let the transformation T : R³ →R² be given by the formula "(x¡ ,xX2,Xz ) = (2x, -x,, x, +3x,). Find…

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Q: Show that arcsech(x) = arctanh(√1-x²) where arcsech(x) is the inverse of f: [0, ∞) → R, f(x) =…

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