# How do you evaluate the definite integral (x^43)e^(-x^(44)) dx for a=0, b=1?

We have to look for a primitive of the function $f \left(x\right) = {x}^{43} {e}^{- {x}^{44}}$
$\frac{d}{\mathrm{dx}} \left({e}^{- {x}^{44}}\right) = {e}^{- {x}^{44}} \left(- 44 {x}^{43}\right)$
So we have a primitive for $f$ (we just have to divide by $- 44$), and we have, for the fundamental theorem of integral calculus:
${\int}_{0}^{1} {x}^{43} {e}^{- {x}^{44}} = {e}^{- {x}^{44}} / \left(- 44\right) {|}_{0}^{1}$$= - \frac{1}{44 e} + \frac{1}{44}$