Help with integral calculus? double integration ...NEED IT ASAP?

Question

1. ∫(from 0 to 1) ∫(from 0 to y^3/2) x/y^2 dxdy

2. ∫(from 0 to 1) ∫(from 0 to x^2) xe^y dydx

3. F(x,y) = -x^2 - 2y^2 + 6x -4y

a.) find max or min

please help me, this is a matter of life and death, hope for you kind heart...

Answer 1

1.

∫(from 0 to 1) ∫(from 0 to y^3/2) x/y^2 dxdy

=∫(from 0 to 1)(1/y^2) ∫(from 0 to y^3/2) x dxdy

=∫(from 0 to 1)(1/y^2) [1/2*x^2](from 0 to y^3/2) dy

=∫(from 0 to 1)(1/y^2) [1/2*y^3] dy

=∫(from 0 to 1)(1/2*y) dy

=1/4(y^2) (from 0 to 1) = 1/4

2. ∫(from 0 to 1) ∫(from 0 to x^2) xe^y dydx

∫(from 0 to 1) x ∫(from 0 to x^2) e^y dydx

∫(from 0 to 1) x [(e^(x^2)) -1 ]dx

∫(from 0 to 1) x (e^(x^2)) dx - ∫(from 0 to 1) x dx

for the first integral, use u=x^2, du=2x dx, or dx= du/(2x)

1/2 ∫(from 0 to 1) e^u du - ∫(from 0 to 1) x dx

=1/2(e-1) - 1/2 = (1/2)e -1

I don't remember how to do the 3rd one, sorry!