Chapter 6.2, Problem 24E

To determine

To evaluate integral

  ${\displaystyle \underset{0}{\overset{b}{\int }}4xdx}$

Answer to Problem 24E

  ${\displaystyle \underset{0}{\overset{b}{\int }}4xdx}=2b^2$

Explanation of Solution

Given:

  ${\displaystyle \underset{0}{\overset{b}{\int }}4xdx};b>0$

Calculation: Consider the integral

  $\begin{array}{l}I={\displaystyle \underset{0}{\overset{b}{\int }}4xdx}\\ =4{\displaystyle \underset{0}{\overset{b}{\int }}xdx}\\ =4{\left[\frac{x^2}{2}\right]}_0^b\\ =2{\left[x^2\right]}_0^b\\ =2\left(b^2-0\right)\\ =2b^2\end{array}$