_0^ /4 ^6 x , ^2 x ,dx = - Vidyadip

MCQ

$\int_0^{\pi /4} {{{\tan }^6}x \, {{\sec }^2}x\,dx = } $

✓
$\frac{1}{7}$
B
$\frac{2}{7}$
C
$1$
D
None of these

✓

Answer

Correct option: A.

$\frac{1}{7}$

a
(a) Put $t = \tan x \Rightarrow dt = {\sec ^2}x\,dx$

Now $\int_0^{\pi /4} {{{\tan }^6}x{{\sec }^2}xdx = \int_0^1 {{t^6}dt = \frac{1}{7}[{t^7}]_0^1 = \frac{1}{7}} } $.

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