Question

How do you find the definite integral of `x * e^ (-x^2) dx` from `[1, sqrt2]`?

Answer 1

`1/2*(e^(-1)-e^(-2))`

Explanation:

`int_1^sqrt2 xe^(-x^2)*dx`

=`-1/2int_1^sqrt2 -2xe^(-x^2)*dx`

=`[-1/2e^(-x^2)]_1^sqrt2`

=`1/2*(e^(-1)-e^(-2))`