If $\smallint f\left( x \right)\cos \,\,x\,dx = \frac{1}{2}\,\,{\left\{ {f\left( x \right)} \right\}^2} + \,\,c,\;\,{\rm{then}}\,\,\;f\left( x \right)$ is

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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\int f\left( x \right)\cos \,\,x\,dx = \frac{1}{2}\,\,{\left\{ {f\left( x \right)} \right\}^2} + \,\,c,\;\,\mathrm{then}\,\,\;f\left( x \right)

View answer and explanation

Correct option: B

\sin \,\,x + c

Option B (

\sin \,\,x + c

) is correct because the derivative of

\frac{1}{2}\{f(x)\} ^2 + c

leads to

f'(x) = \cos x

, and integrating gives

f(x) = \sin x + c