Chapter 6.2, Problem 23E

To determine

To evaluate integral

  ${\displaystyle \underset{0}{\overset{b}{\int }}xdx}$

Answer to Problem 23E

  ${\displaystyle \underset{0}{\overset{b}{\int }}xdx}=\frac{b^2}{2}$

Explanation of Solution

Given:

  ${\displaystyle \underset{0}{\overset{b}{\int }}xdx};b>0$

Calculation: Consider the integral

  $\begin{array}{l}I={\displaystyle \underset{0}{\overset{b}{\int }}xdx}\\ ={\displaystyle \underset{0}{\overset{b}{\int }}xdx}\\ ={\left[\frac{x^2}{2}\right]}_0^b\\ =\left(\frac{b^2}{2}-0\right)\\ =\frac{b^2}{2}\end{array}$