Question

The value of $\underset{-1}{\overset{1}{\int }}{x}^2{e}^{\left[x^3\right]}dx,$ where $\left[t\right]$ denotes the greatest integer $\le t$ ,is :

• A. $\frac{e+1}{3}$
• B. $\frac{e-1}{3e}$
• C. $\frac{e+1}{3e}$
• D. $\frac{1}{3e}$

Answer 1

The correct option is C $\frac{e+1}{3e}$

$I=\underset{-1}{\overset{0}{\int }}{x}^2\times e^{-1}dx+\underset{0}{\overset{1}{\int }}{x}^{2}dx\therefore I=\frac{x^3}{3e}{|}_{-1}^0+\frac{x^3}{3}{|}_0^1\Rightarrow I=\frac{1}{3e}+\frac{1}{3}$