Question

The integral $\mathop \smallint \limits_0^{\pi /2} \,\,f\,\,\left( {\sin \,\,2x} \right)\,\,\sin \,\,x\,\,dx$ is equal to

Accepted Answer

$\mathop \smallint \limits_0^{\pi /2} \,\,f\left( {\sin \,\,2x} \right)\,\,\cos \,\,x\,\,dx = \sqrt 2 \,\,\mathop \smallint \limits_0^{\pi /4} \,\,f\left( {\cos \,\,\,2x} \right)\cos \,\,x\,\,dx$

Answer

$\mathop \smallint \limits_0^{\pi /2} \,\,f\,\,\left( {\cos \,\,2x} \right)\,\,\sin \,\,x\,\,dx = \sqrt 2 \,\mathop \smallint \limits_0^{\pi /2} \,\,f\,\,\left( {\cos \,\,\,2x} \right)\sin \,\,x\,\,dx$

Answer

$\mathop \smallint \limits_0^{\pi /2} \,\,f\left( {\cos \,\,2x} \right)\cos \,\,x\,\,dx = \sqrt 2 \,\,\mathop \smallint \limits_0^{\pi /2} \,\,f\left( {\cos \,\,2x} \right)\,\,\cos \,\,x\,\,dx$

Answer

$\mathop \smallint \limits_0^{0\pi /2} \,\,f\left( {\sin \,\,2x} \right)\,\,\cos \,\,x\,\,dx = \sqrt 2 \,\,\mathop \smallint \limits_0^{\pi /2} \,\,f\left( {\cos \,\,\,2x} \right)\,\,\cos \,\,x\,\,dx$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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