Chapter 7, Problem 6RE

To determine

To find: the area of the region enclosed by the given lines and the curve.

Answer to Problem 6RE

The area of the region enclosed by the given lines and the curve is 1.

Explanation of Solution

Given:

  $y=x,y=0,y=\frac{1}{x^2},x=2$ .

Calculation:

The graph of the area enclosed by the given curves is,

  

Now the required area is,

  $\begin{array}{c}{\displaystyle \underset{0}{\overset{1}{\int }}xdx}+{\displaystyle \underset{1}{\overset{2}{\int }}\frac{1}{x^2}dx}={\left[\frac{x^2}{2}\right]}_0^1+{\left[-\frac{1}{x}\right]}_1^2\\ =\frac{1}{2}\left[1^2-0^2\right]-\left[\frac{1}{2}-\frac{1}{1}\right]\\ =\frac{1}{2}+\frac{1}{2}\\ =1\end{array}$