Jee Main
Definite Integration
JEE Main 2021 (Online) 27th July Morning Shift
INTEGER+4 / -12021
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 _______________.
\(F(x) = {e^{ - x}}\int\limits_3^x {(3{t^2} + 2t + 4F'(t))dt}\). If \(F'(4) = {{\alpha {e^\beta } - 224} \over {{{({e^\beta } - 4)}^2}}}\), then \(\alpha\) + \(\beta\) is equal to _______________.