Find the centroid of the solid

Mdhiggenz

Homework Statement

The solid bounded by the surface z=y2 and the planes x=0,x=1,z=1

I have a question regarding the limits of integration, would it be incorrect, if when I graphed z=y2

I changed it to a familiar xy graph instead I just graphed it as if z was y and x was y.

Pretty much I changed the y axis to z, and x axis to y.

Then graphed the potion z=y2

and included the line z=1

Thanks
Higgenz

The Attempt at a Solution

You can't just "throw away" this x-axis. The graph of $z= y^2$ is a "parabolic cylinder" in three dimensions. Think of it as a "water trough" with parabolic cross section, extended along the x-axis. Of course, the volume is just the area of a cross section times the length.