A) \[\frac{1}{7}\]
B) \[\frac{2}{7}\]
C) 1
D) None of these
Correct Answer: A
Solution :
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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