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For the function f(x) = xx on the interval [-7, 7] we need only compute one set of the Fourier bn = 7 j 0 2/7 (x^2)sin((n pi*x), da bn = 343/(n*pi) (-1)^(n+1)

For the function f(x) = xx on the interval [-7, 7] we need only compute one set of the Fourier bn = 7 j 0 2/7 (x^2)sin((n pi*x), da bn = 343/(n*pi) (-1)^(n+1)

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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The formulae for the Fourier series are often given in the form 1 with the outside the integral. Computing these integrals will often involve u-substitutions, P integration by parts, and other integration techniques that will produce all kinds of constants. With the way these problems are asked in WeBWork, it would be hard to keep track of when constants should be factored out or not, so we will adopt the policy that constants are always part of the integrand. For example the formula for the cosine coefficient would be f(x) cos f(x)cos (1²) dr. When performing an integration by parts, all constants are P included in the u term. bn m²/ ["f(x) cos (TTX). For the function f(x) = xx on the interval [-7, 7] we need only compute one set of the Fourier 7 0 dx. 2/7 (x^2)sin((n*pi*x), da bn = 343/(n*pi) (-1)^(n+1) Note: In the last answer blank, you can include 7, TT, and use cos(n) = (-1)" and make sure you are not including any trigonometric functions, like sin or cos.
Transcribed Image Text:The formulae for the Fourier series are often given in the form 1 with the outside the integral. Computing these integrals will often involve u-substitutions, P integration by parts, and other integration techniques that will produce all kinds of constants. With the way these problems are asked in WeBWork, it would be hard to keep track of when constants should be factored out or not, so we will adopt the policy that constants are always part of the integrand. For example the formula for the cosine coefficient would be f(x) cos f(x)cos (1²) dr. When performing an integration by parts, all constants are P included in the u term. bn m²/ ["f(x) cos (TTX). For the function f(x) = xx on the interval [-7, 7] we need only compute one set of the Fourier 7 0 dx. 2/7 (x^2)sin((n*pi*x), da bn = 343/(n*pi) (-1)^(n+1) Note: In the last answer blank, you can include 7, TT, and use cos(n) = (-1)" and make sure you are not including any trigonometric functions, like sin or cos.
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