Let F:[3,5] → R be a twice differentiable function on (3, 5) such that F(x) = e⁻ˣ∫₃ˣ (3t² + 2t + 4F'(t))dt. If F'(4) = (α e^β - 224)/((e^β - 4)²), then α + β is equal to _ _ _ _ _ _ _ _.

Integral Calculus: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Jul, Morning shift · Q33

JEE Main 202127 Jul, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

Let

F:[3,5] \to R

be a twice differentiable function on (3, 5) such that

F(x) = {e^{ - x}}\int\limits_3^x {(3{t^2} + 2t + 4F'(t))dt}

. If

F'(4) = {{\alpha {e^\beta } - 224} \over {{{({e^\beta } - 4)}^2}}}

, then

\alpha

\beta

is equal to _______________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 Integral Calculus Question with Answer (27 Jul Morning shift, Q33) | JEE Arc