Double Integrals

[smatz17]

First question,
int int y*sin(x^2)dA where D={y=[0,1] and x=[y^2,1]}

I don't know what to do. If I integrate y first i get int 1/2*y^2*sin(x^2)dx but the domain of x has y^2 in it and I don't know what to do with it.

Second question,
Find the volume of the region in te first octant bounded by y^2=4x, 2x+y=4, z=y, and y=0 by computing a double integral.

I'm really struggling with how to set up this integral. Once I set it up, I'm pretty sure I can do it.
Thanks.

 

[BigGlenntheHeavy]

\(\displaystyle 1) \ \int_{0}^{1}\int_{0}^{x^{1/2}}ysin(x^{2}) dy dx\)


\(\displaystyle 2) \ \int_{0}^{2}\int_{y^{2}/4}^{(4-y)/2}y \ dx \ dy \ or \ \int_{0}^{1}\int_{0}^{2\sqrt x}y \ dy \ dx \ + \ \int_{1}^{2}\int_0}^{4-2x}y \ dy \ dx\)