Integral to Infinity of Sine p x Cosine q x over x/Mistake

Source Work

 * Chapter $15$: Definite Integrals
 * Definite Integrals involving Trigonometric Functions: $15.34$

This mistake can be seen in the edition as published by Schaum: ISBN 0-07-060224-7 (unknown printing).

Mistake

 * $\ds \int_0^\infty \frac {\sin p x \cos q x} x \rd x = \begin {cases} 0 & : p > q > 0 \\

\dfrac \pi 2 & : 0 < p < q \\ \dfrac \pi 4 & : p = q > 0 \end {cases}$

Correction
As demonstrated in Integral to Infinity of $\dfrac {\sin p x \cos q x} x$, this is incorrect.

It should be:


 * $\ds \int_0^\infty \frac {\sin p x \cos q x} x \rd x = \begin {cases} \dfrac \pi 2 & : p > q > 0 \\

0 & : 0 < p < q \\ \dfrac \pi 4 & : p = q > 0 \\ \end {cases}$