Find the centroid of the solid

  • Thread starter Mdhiggenz
  • Start date
  • #1
Mdhiggenz
327
1

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

 

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
38,731
8,147
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.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
43,021
970
You can't just "throw away" this x-axis. The graph of [itex]z= y^2[/itex] 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.
 

Suggested for: Find the centroid of the solid

  • Last Post
Replies
6
Views
323
  • Last Post
Replies
1
Views
184
Replies
3
Views
32
Replies
4
Views
166
Replies
11
Views
266
Replies
6
Views
267
  • Last Post
Replies
5
Views
1K
Replies
4
Views
207
Replies
8
Views
365
Top