Question

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

Answer 1

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`