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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