JEE Advance - Mathematics (1990 - No. 3)
Show that $$\int\limits_0^{\pi /2} {f\left( {\sin 2x} \right)\sin x\,dx = \sqrt 2 } \int\limits_0^{\pi /4} {f\left( {\cos 2x} \right)\cos x\,dx} $$
This requires advanced calculus techniques, specifically dealing with trigonometric substitutions and properties of definite integrals.
This problem involves complex number integration.
This problem is best solved using Laplace transforms.
This problem is easily solved using basic trigonometric identities.
This problem is a direct application of the fundamental theorem of calculus.