Chapter 6.2, Problem 26E

To determine

To evaluate integral

  ${\displaystyle \underset{a}{\overset{b}{\int }}3tdt}$

Answer to Problem 26E

  ${\displaystyle \underset{a}{\overset{b}{\int }}3tdt}=\frac{3}{2}\left[b^2-a^2\right]$

Explanation of Solution

Given:

  ${\displaystyle \underset{a}{\overset{b}{\int }}3tdt};0<a<b$

Calculation: Consider the integral

  $\begin{array}{l}I={\displaystyle \underset{a}{\overset{b}{\int }}3tdt}\\ =3{\displaystyle \underset{a}{\overset{b}{\int }}tdt}\\ =3{\left[\frac{t^2}{2}\right]}_a^b\\ =\frac{3}{2}\left[b^2-a^2\right]\end{array}$