Question

Prove the following:

`int_0^1 xe^x dx = 1`

Answer 1

Let  I = `int_0^1 xe^x dx = 1`

On integrating, take x as the first function.

I = `int_0^1 x e^x dx`

`= [x e^x]_0^1 - int_0^1 1 * e^x   dx`

`= e - 0 - 1 [e^x]_0^1`

`= e - (e - 1)`

`= e - e + 1`

= 1