A) 1
B) 2
C) 3
D) 4
Correct Answer: A
Solution :
\[I=2\int\limits_{0}^{\pi }{\frac{dx}{1+{{\tan }^{4}}x}=4\int\limits_{0}^{x/2}{\frac{dx}{1+{{\tan }^{4}}x}}}\] Use King \[I=4\int\limits_{0}^{\pi /2}{\frac{dx}{1+{{\cot }^{4}}x}}\] \[\therefore \,\,2I=4\int\limits_{0}^{\pi /2}{dx=4.\frac{\pi }{2}\,\Rightarrow \,I=\pi }\]You need to login to perform this action.
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