- #1
Neutrinogun
- 9
- 0
[STRIKE][/STRIKE]
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
[itex]y = \sqrt{x-1} , y = 0, x = 5;[/itex] about [itex]y = 3[/itex]
I already completed graphing it, but not really sure how to show that here.
2[itex]\pi[/itex][itex]\int_0^2[/itex](shell radius)(shell height) [itex]dy[/itex]
2[itex]\pi[/itex][itex]\int_0^2[/itex][itex](y)(y^2+1)[/itex] [itex]dy[/itex]
2[itex]\pi[/itex][itex]\int_0^2[/itex][itex](y^3+y)[/itex] [itex]dy[/itex]
[itex]2\pi (((y^4)\div4)) + (y^2)\div2)[/itex]
[itex]2\pi(4+2) - 0[/itex]
[itex]12\pi[/itex]
Is that correct? I'm not sure if I did the shell height correctly.
Homework Statement
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
Homework Equations
[itex]y = \sqrt{x-1} , y = 0, x = 5;[/itex] about [itex]y = 3[/itex]
The Attempt at a Solution
I already completed graphing it, but not really sure how to show that here.
2[itex]\pi[/itex][itex]\int_0^2[/itex](shell radius)(shell height) [itex]dy[/itex]
2[itex]\pi[/itex][itex]\int_0^2[/itex][itex](y)(y^2+1)[/itex] [itex]dy[/itex]
2[itex]\pi[/itex][itex]\int_0^2[/itex][itex](y^3+y)[/itex] [itex]dy[/itex]
[itex]2\pi (((y^4)\div4)) + (y^2)\div2)[/itex]
[itex]2\pi(4+2) - 0[/itex]
[itex]12\pi[/itex]
Is that correct? I'm not sure if I did the shell height correctly.