• Support PF! Buy your school textbooks, materials and every day products Here!

Volume of solid revolving about y-axis

  • Thread starter frumdogg
  • Start date
  • #1
18
0

Homework Statement


Find the volume of the solid generated by revolving the region bounded by the graph of
y = x3 and the line y = x,
between x = 0 and x = 1,
about the y-axis.


Homework Equations



[tex]\pi[/tex][tex]\overline{1}[/tex][tex]\int[/tex][tex]\underline{0}[/tex][R(x)[tex]^{2}[/tex]-[r(x)][tex]^{2}[/tex]dx

The Attempt at a Solution


x^6 - x^2 dx = x^7/7 - x^3/3 is where I get stuck.
 

Answers and Replies

  • #2
41
0
Since you're revolving it around the y axis, you would probably want to integrate the areas with respect to y. Once you do that and find your new limits of integration, there shouldn't be much of a problem getting the answer.

Edit: And don't forget about that Pi in the equation, when you integrated with respect to x you omitted it.
 
Last edited:
  • #3
29
0
yes you want each slice perpendicular to the line you are rotating to. in your case, each slice will be (deltaY) high so you would integrate in terms of y, not x.

then it just becomes the integral of pi(Routside)^2-pi(Rinside)^2dy
 

Related Threads for: Volume of solid revolving about y-axis

Replies
1
Views
488
Replies
1
Views
2K
Replies
1
Views
3K
  • Last Post
Replies
4
Views
548
Replies
2
Views
1K
Replies
5
Views
4K
Replies
3
Views
5K
  • Last Post
Replies
7
Views
5K
Top