Question

Evaluate the definite integral ${\int }_4^5{e}^{x}dx$

Answer 1

Let $I={\int }_4^5{e}^{x}dx$
$\Rightarrow \int e^{x}dx=e^x=F\left(x\right)$
By second fundamental theorem of calculus, we obtain
$I=F\left(5\right)-F\left(4\right)$
$=e^5-e^4$
$=e^4(e-1)$