Chapter 5.4, Problem 190E

Let F. G. and H be differential functions on

$\left[a,b\right],\left[c,d\right]$and $[e,f]$ , respectively, where

a. b. c, d. e, and f are real numbers such that

a

${\displaystyle \underset{a}{\overset{b}{\int }}{\displaystyle \underset{c}{\overset{d}{\int }}{\displaystyle \underset{e}{\overset{f}{\int }}F\text{'}\left(x\right)G\text{'}\left(y\right)H\text{'}\left(z\right)dzdydx}=\left[F\left(b\right)-\left(a\right)\right]\left[G\left(d\right)-G\left(c\right)\right]\left[H\left(f\right)-H\left(e\right)\right]}}$ .