Answer: Show that the given integral represents the
Chapter 11, Problem 11.1.128(choose chapter or problem)
Show that the given integral represents the indicated function. Hint. Use (5), (11), or (13); the integral tells you which one, and its value tells you what function to consider. (Show the details of your work.)
\(\int_{0}^{\infty} \frac{\sin w-w \cos w}{w^{2}} \sin x u^{*} d v\)
=\left\{\begin{array}{clr} \pi x / 2 \text { if } 0<x<1 \\ \pi / 4 \text { if } x=1 \\ 0 \text { if } x>1
\end{array}\right.\)
Text Transcription:
int_{0}^{infty} sin w - w cos w / w^2 sin xu* dv
= {pi x / 2 if 0 < x < 1 \\ pi/4 if x = 1 \\ 0 if x > 1
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