Question

Using properties of the Fourier Sine and Cosine Transforms, show how to obtain the Fourier Sine Transform of the following function f(x) = xe^{-x^2/2}

          Using properties of the Fourier Sine and Cosine Transforms, show how to obtain the Fourier Sine Transform of the following function

f(x) = xe^{-x^2/2}

Using properties of the Fourier Sine and Cosine Transforms, show how to obtain the Fourier Sine Transform of the following function

f(x) = xe^-x^2/2

Added by Vicenta C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/13/2023

Step 1

The function is given as: f(x) = ce^(x^2/2) The Fourier Sine Transform (FST) is defined as: FST[f(x)] = F_s(k) = \int_0^\infty f(x) \sin(kx) dx So, we need to find the integral: F_s(k) = \int_0^\infty ce^{x^2/2} \sin(kx) dx This integral is not easy to solve Show more…

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Using properties of the Fourier Sine and Cosine Transforms, show how to obtain the Fourier Sine Transform of the following function f(x) = xe^{-x^2/2}

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