If ∫ (sin^3x)e^sin^2x dx x ∈ [0, π]= α - β/e ∫√t e^t dt x ∈ [0,1] ​ then α + β is equal to ...... . ​

Question

If \(\displaystyle \int_0^{\pi}\)(sin³ x)e^{-sin^2x} dx = α - \(\frac{\beta}{e}\) \(\displaystyle \int^1_0 \sqrt{t} e^t dt\), then \(\alpha + \beta\) is equal to ...... .

∫(sin^3x)e^{sin^2x} dx  x ∈ [0, π]= α - β/e ∫√t e^t dt x ∈ [0,1] ​ ​

Answer 1

Correct answer 5

Hence, α + β = 5