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Prove that for any integer NTX sin? dx = L. -L

Prove that for any integer NTX sin? dx = L. -L

Advanced Engineering Mathematics
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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Prove that for any integer n NTX sin? (") dx = L. L -L Find the Fourier series of the function f(x) = sin (T) on the interval [-L, L]. Find the Fourier sine series of the function f (x) = x² cos x on the interval [-L, L]. Find the Fourier series of the function f(x) = 2L – ; on the interval [-L, L]. Denote the second Fourier cosine coefficient on the interval [-L, L] by L 27x A2 : f (x) cos -dx. -L Show that for the function f (x) = eLa 2L3 sinh(L²). A2 = L4 + A72
Transcribed Image Text:Prove that for any integer n NTX sin? (") dx = L. L -L Find the Fourier series of the function f(x) = sin (T) on the interval [-L, L]. Find the Fourier sine series of the function f (x) = x² cos x on the interval [-L, L]. Find the Fourier series of the function f(x) = 2L – ; on the interval [-L, L]. Denote the second Fourier cosine coefficient on the interval [-L, L] by L 27x A2 : f (x) cos -dx. -L Show that for the function f (x) = eLa 2L3 sinh(L²). A2 = L4 + A72
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