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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^{\pi / 4} \tan ^6 x \sec ^2 x d x=$
  • ✓
    $\frac{1}{7}$
  • B
    $\frac{2}{7}$
  • C
    1
  • D
    $\frac{3}{7}$
✓

Answer

Correct option: A.
$\frac{1}{7}$
(A)
Put $\tan x= t \Rightarrow \sec ^2 x d x= dt$
When $x=0, t =0$ and when $x=\frac{\pi}{4}, t =1$
$\therefore \quad \int_0^{\pi / 4} \tan ^6 x \sec ^2 x d x=\int_0^1 t ^6 dt =\frac{1}{7}\left[ t ^7\right]_0^1=\frac{1}{7}$

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