|0->1 |y->1 e^x^2dxdy?

Question

Reversing the order of integration

Answer 1

Draw a picture of the region of integration. It is a triangle with vertices at (0,0), (1,0), and (1,1). If we do y-integration first, this region is described by 0 < y < x, 0 < x < 1

So the integral becomes

(integral, x from 0 to 1)(integral, y from 0 to x) e^(x²) dy dx

Doing the y-integration leaves

(integral from 0 to 1) x e^(x²) dx

which is straightforward to do.