Question

evaluate the definite integral [0,1] xe^(-x^2)dx and please show steps

Answer 1

xe^(-x^2)dx = -(1/2) *-2xe^(-x^2)dx
substitute with u=-x^2
-1/2 Int[e^u,du] = -(1/2) e^u = -(1/2) * e^(-x^2)

Answer 2

Evaluate
(-(1/2) * e^(-1^2)) - (-(1/2) * e^((-0)^2)) = -1/(2e) + 1/2