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Question: Answered & Verified by Expert
$\int_0^{\pi / 6} \frac{\sin x}{\cos ^3 x} d x=$
MathematicsDefinite IntegrationJEE Main
Options:
  • A $\frac{2}{3}$
  • B $\frac{1}{6}$
  • C 2
  • D $\frac{1}{3}$
Solution:
1322 Upvotes Verified Answer
The correct answer is: $\frac{1}{6}$
Let $I=\int_0^{\pi / 6} \frac{\sin x}{\cos ^3 x} d x=\int_0^{\pi / 6} \tan x \sec ^2 x d x$
Put $t=\tan x \Rightarrow d t=\sec ^2 x d x$, then we have
$I=\int_0^{\frac{1}{\sqrt{3}}} t d t=\left[\frac{t^2}{2}\right]_0^{\sqrt{3}}=\frac{1}{6}$

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