If $f\left( x \right) = \cos \,\,x\,\, - \,\,{\cos ^2}\,x\,\, + \,\,{\cos ^3}\,\,x\,\, - ...\;\infty $, then $\smallint f\left( x \right)dx$ is equal to

$x - \,\,\frac{1}{2}\,\,\tan \,\,\frac{x}{2} + c$

$\frac{{x - \tan \,\,\frac{x}{2}}}{2} + c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

f\left( x \right) = \cos \,\,x\,\, - \,\,{\cos ^2}\,x\,\, + \,\,{\cos ^3}\,\,x\,\, - ...\;\infty

, then

\int f\left( x \right)dx

is equal to

View answer and explanation

Correct option: B

x - \,\,\tan \,\,\frac{x}{2} + c

Option B (

x - \,\,\tan \,\,\frac{x}{2} + c

) is correct because the given series is a geometric progression that can be simplified and integrated.