Question

$\frac{d}{{dx}}\,\,\left( {\mathop \smallint \limits_{f\left( x \right)}^{g\left( x \right)} \,\,\phi \,\,\left( t \right)\,\,dt} \right)$ is equal to

Accepted Answer

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

Answer

$\phi \,\,\left( {\,g\left( x \right)} \right)\,\, - \,\,\phi \,\,\left( {\,f\left( x \right)} \right)$

Answer

$\frac{1}{2}\,\,{\left[ {\,\phi \left( {\,g\,\,\left( x \right)} \right)} \right]^2}\,\, - \,\,\frac{1}{2}\,\,{\left[ {\,\phi \left( {\,f\,\,\left( x \right)} \right)} \right]^2}$

Answer

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

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

More Questions from DEFINITE INTEGRATION