Question

Evaluate the integral of xe^(x²) dx from 0 to 1

Answer 1

$\int_0^1xe^{x^2}dx = [x^2 = u, 2xdx=du, xdx=\cfrac{1}{2}du, 1\to1,0\to0] =\\ =\cfrac{1}{2}\int_0^1e^udu = \cfrac{1}{2}e^u|_0^1 = \cfrac{e-1}{2}$