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Definite Integration question

2021 · 27 Jul · Shift 1 · Q44

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PYQ Library
JEE Main
Mathematics
Definite Integration
2021 · 27 Jul · Shift 1 · Q44

Definite Integration question

2021 · 27 Jul · Shift 1 · Q44

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

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

\underline{\hspace{2cm}}

.

Numerical answer

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