Question

How do you integrate `int2xe^x dx` from 0 to 1?

Answer 1

By parts:

`int_a^b 2xe^xdx = uv - int_a^bvdu`

Let u = `2x` and v = `e^x`.
`du` = `2dx`

`int_0^1 2xe^x dx = (2x*e^x) - int_0^1e^x*2 dx`
`= [(2x*e^x) - 2int_0^1e^x dx] eval (0->1)`
`= [2(1)e^(1) - 2(0)e^(0)] - 2(e^1 - e^0)`
`= [2e] - 2e + 2`
`= 2`