Chapter 8.5, Problem 2QR

To determine

To find the value of the integral ${\displaystyle \underset{0}{\overset{1}{\int }}{e}^{x}dx}$ by finding the anti-derivative.

Answer to Problem 2QR

The value of the integral is $e^1-1$ .

Explanation of Solution

Given information: ${\displaystyle \underset{0}{\overset{1}{\int }}{e}^{x}dx}$

Formula used: ${\displaystyle \int e^{x}dx}=e^x$

Calculation :

The given integral is

  ${\displaystyle \underset{0}{\overset{1}{\int }}{e}^{x}dx}={\left[e^x\right]}_0^1=e^1-1$

Hence, the value of the integral is $e^1-1$ .