The value of _0^1 x^2 e^x dx is equal to - Vidyadip

MCQ

The value of $\int_0^1 {{x^2}{e^x}dx} $ is equal to

✓
$e - 2$
B
$e + 2$
C
${e^2} - 2$
D
${e^2}$

✓

Answer

Correct option: A.

$e - 2$

a
(a) We have, $I = \int_0^1 {{x^2}{e^x}dx} $

==> $I = [{x^2}.{e^x}]_0^1 - \int_0^1 {2x.{e^x}dx} $

==> $I = e - 2[x{e^x} - {e^x}]_0^1$

==>$I = e - 2\,[e - e - (0 - 1)]$

==> $I = e - 2$.

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