Chapter 14.4B, Problem 7GCE

To determine

To find:

The area of the region bounded by the curve.

Explanation of Solution

Given:

The vertical lines

  $x=-4$ and $x=4$

Concept used:

  $f\left(x\right)$ and $g\left(x\right)$ be continuous functions over an interval $\left[a,b\right]$ and R denoted the region between the graph of $f\left(x\right)$ and $g\left(x\right)$ and bounded on the left and right by the lines $x=a$

  $A={\displaystyle \underset{a}{\overset{b}{\int }}\left|f\left(x\right)-g\left(x\right)\right|dx}$

Calculation:

The standard normal distribution

  $f\left(x\right)=\frac{1}{\sqrt{2\pi }}{e}^{-\frac{x^2}{2}}$

Test one point in each of the region formed by the graph.

If the point satisfies the function then shade the entire region to denote that every point in the region satisfies the function.

To draw the table

$x-axis$	$-4$	$4$	$-2$	$2$
$y-axis$	$0$	$0$	$0$	$0$

Draw the graph

  $x=-4$ and $x=4$