Let F : [3, 5] → R be a twice differentiable function on (3, 5) such that f(x) = e^-x ∫ (3t^2 + 2t + 4f'(t)) dt x ∈ [3,x]

Question

Let F : [3, 5] → R be a twice differentiable 

function on (3, 5) such that 

f(x) = e^-x  \(\int \limits_3^x\)(3t² + 2t 4F' (t)) dt.

If F'(4) = \(\frac{\alpha e^\beta - 224}{(e^\beta - 4)^2}\), then \(\alpha+ \beta \) is equal to ........... .

Answer 1

correct answer 16

f(3) = 0

Now put value of x = 4 we will get \(\alpha\) = 12 & \(\beta\) = 4