_0^1 e ^ 2 x dx = - Vidyadip

MCQ

$\int_0^1 e ^{2 \log x} dx =$

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

✓

Answer

Correct option: C.

$\frac{1}{3}$

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

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