integrate e^-xdx over the interval [0,1]
when x= 0, u=?
when x = 1, u = ?
First, you may note that , and therefore that by the Chain Rule.
When and , we want the derivative to end up with the positive coefficient instead of . To do this, we add a as a coefficient to the antiderivative so that we will end up with :
The general antiderivative is therefore .
Alternatively, we could let