Let f be a differentiable function satisfying f(x)=2/(√(3)) ∫₀^(√(3)) f((λ² x)/3) d λ, x>0 and f(1)=√(3). If y=f(x) passes through the point (α, 6), then α is equal to _ _ _ _ _ _ _.

Integral Calculus: JEE Main 2022 Mathematics question

JEE Main 2022 · 27 Jul, Evening shift · Q30

JEE Main 202227 Jul, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

Let f be a differentiable function satisfying

f(x)=\frac{2}{\sqrt{3}} \int\limits_{0}^{\sqrt{3}} f\left(\frac{\lambda^{2} x}{3}\right) \mathrm{d} \lambda, x>0

and

f(1)=\sqrt{3}

. If

y=f(x)

passes through the point

(\alpha, 6)

, then

\alpha

is equal to _____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2022 Integral Calculus Question with Answer (27 Jul Evening shift, Q30) | JEE Arc