Question

Determine a positive integer n ≤ 5, such that ∫e^x(x – 1)ⁿ dx for x ∈ [0,1] = 16 – 6e.

Answer 1

Given integral 

= 1 – (e – 1) = 2 – e

From Eq. (i), we can write 

I₂ = – 1 – 2I₁ 

= – 1 – 2(2 – e) = 2e – 5 

Again, from Eq. (i), we can write 

I₃ = 1 – 3I₂ 

= 1 – 3(2e – 5) = 16 – 6e