Math
posted by Anonymous on .
If f(x) is an antiderivative (i.e. primitive) of x*e^(x^2) and f(0)=1. Then f(1)=?

let u = x^2
we have
f = 1/2∫e^u du
f(x) = 1/2 e^(x^2) + C
1 = 1/2 (1) + C
C = 3/2
f(x) = 1/2 e^(x^2) + 3/2
f(1) = 1/2 * 1/e + 3/2
= 1/2 (3  1/e)