Question

Evaluate the following
(a medal will be given to first with quality steps, don't need to show past the integration phase where you're substituting 1& 0 in for x unless you just feel like it):
\[\huge \int\limits_{0}^{1} x^2e^{-x^3} dx\]

Answer 1

Should you just let u = - x^3
-> -1/3 Int e^u du

Answer 2

Let u=x^3, then du = 3x^2 dx, and the integral becomes
1/3 \[\int\limits_{0}^{1} e^{-u} du\] = 1/3.

Answer 3

Wonderful, thank you both!

Answer 4

:)