(a) Evaluate the integral 1 eteinxx dx where i = V-1 and n + 0. Simplify your result as much as possible. (b) Use your result from part (a) to expand the function f(x) = e* on the interval (0, 1) in %3D a Fourier sine series.
(a) Evaluate the integral 1 eteinxx dx where i = V-1 and n + 0. Simplify your result as much as possible. (b) Use your result from part (a) to expand the function f(x) = e* on the interval (0, 1) in %3D a Fourier sine series.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Fourier Series Question
![(a) Evaluate the integral
\[
\int_{0}^{1} e^{x} e^{in\pi x} \, dx
\]
where \( i = \sqrt{-1} \) and \( n \neq 0 \). Simplify your result as much as possible.
(b) Use your result from part (a) to expand the function \( f(x) = e^{x} \) on the interval \( (0, 1) \) in a Fourier sine series.
(c) Sketch the graph of this series on the interval \((-2, 2)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3aacacdb-b1cd-42a5-b00f-4ebef102db2d%2F48b0caa6-b300-4589-b38f-52378d2e9680%2F0pg2mt5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Evaluate the integral
\[
\int_{0}^{1} e^{x} e^{in\pi x} \, dx
\]
where \( i = \sqrt{-1} \) and \( n \neq 0 \). Simplify your result as much as possible.
(b) Use your result from part (a) to expand the function \( f(x) = e^{x} \) on the interval \( (0, 1) \) in a Fourier sine series.
(c) Sketch the graph of this series on the interval \((-2, 2)\).
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