Let {F}:[3,5] \\to{R} be a twice differentiable function on (3,5) such that {F}({x})={e}^{-{x}} \\int_{3} ^{{x}}(3 {t}^{2}+2 {t}+4 {F}'({t})) {dt} If F'(4)={\\alpha {e}^{\\beta}-224}/{({e}^{\\beta}-4)^{2}}, then \\alpha+\\beta is equal to _________. [27 Jul 2021 Shift 1]

Definite Integrals Part 2

Section: Mathematics

Question : 72 of 100

Marks: +1, -0

Let F:[3,5]→R be a twice differentiable function on (3,5) such that
F(x)=e−x‌

∫

(3t2+2t+4F′(t))dt
If F′(4)=

αeβ−224

(eβ−4)2

, then α+β is equal to _________.

[27 Jul 2021 Shift 1]

Go to Question:

Prev Question

Next Question