_0^1 e^ 2 , In ,x ,dx = - Vidyadip

MCQ

$\int_0^1 {{e^{2\,{\rm{In}}\,x}}\,dx} = $

A
$0$
B
$\frac{1}{2}$
✓
$\frac{1}{3}$
D
$\frac{1}{4}$

✓

Answer

Correct option: C.

$\frac{1}{3}$

c
(c)$\int_0^1 {{e^{2\log x}}dx = \int_0^1 {{e^{\log {x^2}}}} dx = \int_0^1 {{x^2}dx = \left[ {\frac{{{x^3}}}{3}} \right]_0^1 = \frac{1}{3}} } $.

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