If $\smallint f\,\,\left( x \right)\,\,dx = {\rm{g}}\,\,\left( x \right)$, then $f\,\,\left( x \right)\,\,{\rm{g}}\left( x \right)$ is equal to

$\frac{1}{2}\,\,{{\rm{g}}^2}\left( x \right)$

$\frac{1}{2}\,\,{f^2}\,\left( x \right)$

$\frac{1}{2}\,\,{\left[ {{\rm{g'}}\,\,\left( x \right)} \right]^2}$

$f'\,\,\left( x \right)\,{\rm{g}}\,\,\left( x \right)$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int f\,\,\left( x \right)\,\,dx = \mathrm{g}\,\,\left( x \right)

, then

f\,\,\left( x \right)\,\,\mathrm{g}\left( x \right)

is equal to

View answer and explanation

Correct option: B

\frac{1}{2}\,\,{\mathrm{g}^2}\left( x \right)

Option B (

\frac{1}{2}\,{\mathrm{g}^2}\left( x \right)

) is correct because after applying integration by parts and simplifying, the result matches this option.