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

1 Answer
May 24, 2015

We have to look for a primitive of the function f(x)=x^43e^{-x^44}

For the chain rule,

d/dx(e^{-x^44})=e^{-x^44}(-44x^43)

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_0^1x^43e^{-x^44}=e^{-x^44}/(-44)|_0^1=-1/(44e)+1/44