Chapter 6.4, Problem 28E

To determine

To evaluate the given integral.

Answer to Problem 28E

  ${\displaystyle \underset{2}{\overset{-1}{\int }}{3}^{x}dx}=-7.8887$

Explanation of Solution

Given:

  ${\displaystyle \underset{2}{\overset{-1}{\int }}{3}^{x}dx}$

Calculation:

  $\begin{array}{l}{\displaystyle \underset{2}{\overset{-1}{\int }}{3}^{x}dx}={\left[\frac{3^x}{\ln 3}\right]}_2^{-1}\\ =\frac{1}{\ln 3}\left[3^{-1}-3^2\right]\\ =\frac{1}{\ln 3}\left[\frac{1}{3}-9\right]\\ =\frac{1}{\ln 3}\left[-\frac{26}{3}\right]\\ =-7.8887\end{array}$