Question

Determine a positive integer n ≤ 5, such that ∫ex(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