Double Integrals over General Region

[zm500]

Homework Statement

Find the Volume of the given solid
Bounded by the cylinders y^2+z^2=4 and x=2y, x=0,z=0 in the first octant

Homework Equations

double integral over a region D with f(x,y) dA

The Attempt at a Solution

I graphed it in a xyz plane and got these intervals
D = {(x,y)| 0\leqx\leq4;x/2\leqy\leq2}

where f(x,y) = \sqrt{}4-y^2 with respect to dydx

I don't know how to integrate this!

 

[Char. Limit]

You could try integrating in reverse order, if that would help. If not, just try a substitution, like y=2sin(u).

 

[zm500]

Thank You Very Much.
Reversing order did the trick.

 

[Char. Limit]

Have a great day!