x sin nx dx 2 n 2 n , , n is odd n is even
Chapter 8, Problem 111(choose chapter or problem)
Integrals Used to Find Fourier Coefficients In Exercises 111 and 112 , verify the value of the definite integral, where n is a positive integer.
\(\int_{-\pi}^{\pi} x \sin n x d x=\left\{\begin{array}{cc}\frac{2 \pi}{n}, & n \text { is odd } \\ -\frac{2 \pi}{n}, & n \text { is even }\end{array}\right\).
Text Transcription:
int_-pi^pi x sin nx dx=2 pi/n, -2 pi/n
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