A community for students.
Here's the question you clicked on:
 0 viewing
 3 years ago
Find the volume of the solid obtained by rotating the region bounded by x=0 and x = 9y^2 about the line x=1
 3 years ago
Find the volume of the solid obtained by rotating the region bounded by x=0 and x = 9y^2 about the line x=1

This Question is Closed

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1330221858790:dwI think judging by the picture the way to go is the socalled 'washer method' the graph of x=9y^2 intersects the line x=0 at y=3 and y=3, so those will be our bounds of integration now for the radii...

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1330222034408:dwthe outer radius will be from x=1 to f(y), so the distance is ro=f(y)(1) the inner radius is from x=1 to the xaxis, so that is 1 here is an overhead view of each washer that we will usedw:1330222180739:dwso the integral will be\[\pi\int_{a}^{b}r_o^2r_i^2dy=\pi\int_{3}^{3}(f(y)+1)^21^2dy\]\[=\pi\int_{3}^{3}(10y)^21dy\]

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.2whoops, typo on the last integral (forgot to that y is squared): \[V=\pi\int_{a}^{b}r_o^2r_i^2dy=\pi\int_{3}^{3}(f(y)+1)^21^2dy\]\[V=\pi\int_{3}^{3}(10y^2)^21dy\]and since this integrand is even we can write\[V=2\pi\int_{0}^{3}(10y^2)^21dy\]

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.5Thanks Turing. You are awesome!!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.