Q80 / 150 · MHT CET 2022 (08 Aug Shift 1) · Mathematics

$\int_0^{\frac{\pi}{4}} \sec ^4 x d x=$

  • A
    $\frac{2}{3}$
  • B
    $\frac{1}{3}$
  • Correct answer
    C
    $\frac{4}{3}$
  • D
    1

Solution

$\begin{aligned} & \int_0^{\frac{\pi}{4}} \sec ^4 x \mathrm{~d} x=\int_0^{\frac{\pi}{4}}\left(\tan ^2 x+1\right) \sec ^2 x \mathrm{~d} x \\ & =\left[\frac{\tan ^3 x}{3}+\tan x\right]_0^{\frac{\pi}{4}} \\ & =\frac{1}{3}+1 \\ & =\frac{4}{3}\end{aligned}$

Hence, the correct answer is option: 'C'.

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