_ ^ e^ x^2 x ;dx is equal to - Vidyadip

MCQ

$\int_{}^{} {{e^{{x^2}}}x\;dx} $ is equal to

A
${e^{{x^2}}}$
✓
$\frac{1}{2}{e^{{x^2}}}$
C
$2{e^{{x^2}}}$
D
$\frac{{{e^{{x^2}}} - {x^2}}}{2}$

✓

Answer

Correct option: B.

$\frac{1}{2}{e^{{x^2}}}$

b
(b)$\int_{}^{} {{e^{{x^2}}}.x\,dx} = \frac{1}{2}\int_{}^{} {(2x){e^{{x^2}}}dx} $

(Put ${x^2} = t \Rightarrow dt = 2x\,dx)$.

$ = \frac{1}{2}\int_{}^{} {{e^t}dt} = \frac{1}{2}{e^t} = \frac{1}{2}{e^{{x^2}}}$,

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