Chapter 6, Problem 20RE

To determine

To evaluate the given integral.

Answer to Problem 20RE

  ${\displaystyle \underset{1}{\overset{2}{\int }}\frac{4}{x^2}dx}=2$

Explanation of Solution

Given:

  ${\displaystyle \underset{1}{\overset{2}{\int }}\frac{4}{x^2}dx}$

Calculation:

  $\begin{array}{l}{\displaystyle \underset{1}{\overset{2}{\int }}\frac{4}{x^2}dx}=4{\displaystyle \underset{1}{\overset{2}{\int }}{x}^{-2}dx}\\ =4{\left[\frac{x^{-2+1}}{-2+1}\right]}_1^2\\ =-4{\left[\frac{1}{x}\right]}_1^2\\ =-4\left[\frac{1}{2}-\frac{1}{1}\right]\\ =-4\left[-\frac{1}{2}\right]\\ =2\end{array}$