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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^{\pi / 4} \tan ^2 x d x=$
  • ✓
    $1-\frac{\pi}{4}$
  • B
    $1+\frac{\pi}{4}$
  • C
    $\frac{\pi}{4}-1$
  • D
    $\frac{\pi}{4}$
✓

Answer

Correct option: A.
$1-\frac{\pi}{4}$
(A)
$\int_0^{\pi / 4} \tan ^2 x d x=\int_0^{\pi / 4}\left(\sec ^2 x-1\right) d x$
$\begin{array}{l}=[\tan x]_0^{\frac{\pi}{4}}-[x]_0^{\frac{\pi}{4}} \\ =1-\frac{\pi}{4}\end{array}$

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