A) 1
B) 0
C) \[\frac{1}{4}\]
D) \[\frac{1}{2}\]
E) \[-\frac{1}{4}\]
Correct Answer: C
Solution :
\[f(x)=\tan x-{{\tan }^{3}}x+{{\tan }^{5}}x-....\infty \] \[f(x)=\frac{\tan x}{1+{{\tan }^{2}}x}=\frac{\tan x}{{{\sec }^{2}}x}=\frac{\sin 2x}{2}\] \[\therefore \] \[\int_{0}^{\pi /4}{f(x)}dx=\int_{0}^{\pi /4}{\frac{\sin 2x}{2}}\] \[=\left[ -\frac{\cos 2x}{4} \right]_{0}^{\pi /4}\] \[=\frac{1}{4}\]You need to login to perform this action.
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