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Question: Answered & Verified by Expert
$\int_0^{\frac{\pi}{4}} \sec ^4 x d x=$
MathematicsDefinite IntegrationMHT CETMHT CET 2022 (08 Aug Shift 1)
Options:
  • A $\frac{2}{3}$
  • B $\frac{1}{3}$
  • C $\frac{4}{3}$
  • D 1
Solution:
1081 Upvotes Verified Answer
The correct answer is: $\frac{4}{3}$
$\begin{aligned} & \int_0^{\frac{\pi}{4}} \sec ^4 x \mathrm{~d} x=\int_0^{\frac{\pi}{4}}\left(\tan ^2 x+1\right) \sec ^2 x \mathrm{~d} x \\ & =\left[\frac{\tan ^3 x}{3}+\tan x\right]_0^{\frac{\pi}{4}} \\ & =\frac{1}{3}+1 \\ & =\frac{4}{3}\end{aligned}$

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