Chapter 8.2, Problem 46E

To determine

To Find:

To identify whether the given statement is true, sometimes true or never true.

Answer to Problem 46E

The given statement is sometimes true.

Explanation of Solution

Given information:

The area of the region between the graphs of the continuous functions $y=f\left(x\right)$ and $y=g\left(x\right)$ and the vertical lines $x=a$ and $x=b$

  $\left(a<b\right)$ .

The area A of the region bounded the curves $y=f\left(x\right)$ and $y=g\left(x\right)$ and the vertical lines $x=a$ and $x=b$ is

  ${\displaystyle \underset{a}{\overset{b}{\int }}\left[f\left(x\right)-g\left(x\right)\right]}dx$

This statement is sometimes true, only if $f\left(x\right)\ge g\left(x\right)$ when $a\le x\le b$ .

Therefore, the given statement is sometimes true.