_0^ / 4 ^6 x ^2 x d x=

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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