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 $\displaystyle (x,y)$ with $\displaystyle x^2+y^2<1$ in the first quadrant, then the height of the surface of the solid above this point is $\displaystyle y$ and all points from $\displaystyle (x,y,0)$ to $\displaystyle (x,y,y)$ are in the solid, so the required volume is:
$\displaystyle
V=\int_{x=0}^1 \int_{y=0}^{\sqrt{1-x^2}} y~dy~dx
$
RonL