If $f\,\,\left( x \right) = \tan x\,\, - \,\,{\tan ^3}x\,\, + \,\,{\tan ^5}\,\,x\,\, - ...\,\infty \,\,{\rm{with}}\,\,0\,\, < \,\,x\,\, < \,\,\frac{\pi }{4},\,\,{\rm{then}}\mathop {\,\,\smallint }\nolimits_0^{\pi /4} \,\,f\,\,\left( x \right)\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

f\,\,\left( x \right) = \tan x\,\, - \,\,{\tan ^3}x\,\, + \,\,{\tan ^5}\,\,x\,\, - ...\,\infty \,\,\mathrm{with}\,\,0\,\, < \,\,x\,\, < \,\,\frac{\pi }{4},\,\,\mathrm{then}\mathop {\,\,\int }\nolimits_0^{\pi /4} \,\,f\,\,\left( x \right)\,\,dx

is equal to

View answer and explanation

Correct option: C

\frac{1}{4}

Option C (

\frac{1}{4}

) is correct because the function simplifies to

\frac{{\sin \,2x}}{2}

, and its integral from 0 to

\frac{\pi}{4}

\frac{1}{4}

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