Chapter 8.5, Problem 1QR

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 1QR

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

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

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

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