Math Help - Double Integral Over General Regions Problem

1. Double Integral Over General Regions Problem

I am not sure what to do here

Find the volume of the solid bounded by the cylinder x^2 + y^2 = 1 and the planes y = z, x = 0, z = 0 in the first octant.

Any help would be appreciated.

2. Originally Posted by machi4velli
I am not sure what to do here

Find the volume of the solid bounded by the cylinder x^2 + y^2 = 1 and the planes y = z, x = 0, z = 0 in the first octant.

Any help would be appreciated.
The region is defined by (if I have done this correctly):

Consider the point $(x,y)$ with $x^2+y^2<1$ in the first quadrant, then the height of the surface of the solid above this point is $y$ and all points from $(x,y,0)$ to $(x,y,y)$ are in the solid, so the required volume is:

$
V=\int_{x=0}^1 \int_{y=0}^{\sqrt{1-x^2}} y~dy~dx
$

RonL