If f: R → R be a continuous function satisfying ∫₀^((π)/2) f(sin 2 x) sin x d x+α ∫₀^((π)/4) f(cos 2 x) cos x d x=0, then the value of α is:

Integral Calculus: JEE Main 2023 Mathematics question

JEE Main 2023 · 11 Apr, Evening shift · Q3462

JEE Main 202311 Apr, Evening shiftMathematicsHardIntegral Calculus369× since 2002

f: \mathbb{R} \rightarrow \mathbb{R}

be a continuous function satisfying

\int_\limits{0}^{\frac{\pi}{2}} f(\sin 2 x) \sin x d x+\alpha \int_\limits{0}^{\frac{\pi}{4}} f(\cos 2 x) \cos x d x=0

, then the value of

\alpha

is :

JEE Main 2023 · 11 Apr, Evening shift · Q3462

JEE Main 202311 Apr, Evening shiftMathematicsHardIntegral Calculus369× since 2002

f: \mathbb{R} \rightarrow \mathbb{R}

be a continuous function satisfying

\int_\limits{0}^{\frac{\pi}{2}} f(\sin 2 x) \sin x d x+\alpha \int_\limits{0}^{\frac{\pi}{4}} f(\cos 2 x) \cos x d x=0

, then the value of

\alpha

is :