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

Homework Equations

The Attempt at a Solution

 

[haruspex]

Of course it's valid to relabel the axes if that helps you to picture it. But it's hard to tell whether you've done this correctly unless you restate the problem, word for word, using the new labels.
And don't forget to translate back when you have the answer.

 

[HallsofIvy]

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.