Question

The value of $\underset{2}{\overset{4}{\int }}{e}^{\left[x\right]}dx$ equals to
(where $[.]$ denotes $G.I.F.$)

• A. $e^2$
• B. $e^3$
• C. $e^2+e^3$
• D. $e+e^2$

Answer 1

The correct option is C $e^2+e^3$

$\underset{2}{\overset{4}{\int }}{e}^{\left[x\right]}dx=\underset{2}{\overset{3}{\int }}{e}^{2}dx+\underset{3}{\overset{4}{\int }}{e}^{3}dx=e^2(3-2)+e^3(4-3)=e^2+e^3$