_0^ / 6 x ^3 x d x= - Vidyadip

MCQ

$\int_0^{\pi / 6} \frac{\sin x}{\cos ^3 x} d x=$

A
$\frac{2}{3}$
✓
$\frac{1}{6}$
C
2
D
$\frac{1}{3}$

✓

Answer

Correct option: B.

$\frac{1}{6}$

(B)
Let $I =\int_0^{\pi / 6} \frac{\sin x}{\cos ^3 x} d x=\int_0^{\frac{\pi}{6}} \tan x \sec ^2 x d x$
Put $\tan x= t \Rightarrow \sec ^2 x d x= dt$
When $x=0, t =0$ and when $x=\frac{\pi}{6}, t =\frac{1}{\sqrt{3}}$
$\therefore \quad I =\int_0^{\frac{1}{3}} tdt =\left[\frac{ t ^2}{2}\right]_0^{\frac{1}{\sqrt{3}}}=\frac{1}{6}$

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