First we integrate the corresponding indefinite integral using integration by parts. We find that
xex – ex + C
is the family of all antiderivatives of xex, we can get one particular antiderivative by taking C = 0. Then we can use the resulting antiderivative
xex – ex
in the FTC.
u = x
v' = ex
u' = 1
v = ex.
Then we apply the formula, keeping the limits of integration:
Finally we evaluate each term from 0 to 1:
It's reassuring that we got the same answer we got with Way 1.
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