Evaluate the following integral.

${\displaystyle \underset{1}{\overset{4}{}}}{e}^{x}dx$

Solution

The function $f(x)=e^x$ is continuous everywhere, and we know that an antiderivative is $f(x)=e^x,3,$

${\displaystyle \underset{1}{\overset{4}{}}}{e}^{x}dx=F(4)-F(1)=$

Notice that part two of the fundamental theorem of calculus says we can use any antiderivative Fo