Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
monroe17
Group Title
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=3sqrt(x) and y=3x^2 about the yaxis
 one year ago
 one year ago
monroe17 Group Title
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=3sqrt(x) and y=3x^2 about the yaxis
 one year ago
 one year ago

This Question is Closed

NoelGreco Group TitleBest ResponseYou've already chosen the best response.0
What are the points of intersection?
 one year ago

yakeyglee Group TitleBest ResponseYou've already chosen the best response.1
For two functions \(f\) and \(g\) where \(f \ge g\), the volume between \(x=a\) and \(x=b\) by the cylindrical shells method is given by the following formula. You find those bounds by finding the points of intersection of \(f\) and \(g\), presumably. \[V=2\pi \int_a^b x (fg) dx\]
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.0
0 and 1 are the points of intersection.. but I can't seem to figure out the function to evaluate the integral at ;/
 one year ago

NoelGreco Group TitleBest ResponseYou've already chosen the best response.0
dw:1361312140525:dw Each shell is going to have the shape of a rectangle when it is unfolded from the circular shell shape. You are really looking for the volume of that rectangle. V = length X height X thickness The thickness is going to be dx or dy, the height is the difference between the two functions, and the length is the circumference of each shell.
 one year ago

yakeyglee Group TitleBest ResponseYou've already chosen the best response.1
Using the formula, we have \(f=3\sqrt x\) and \(g=3x^2\). So\[V=2\pi \int_a^b x (3 \sqrt x + 3x^2) dx.\]You can simplify and integrate that, yes?
 one year ago

yakeyglee Group TitleBest ResponseYou've already chosen the best response.1
I should have put \(\displaystyle \int_0^1\), but you get the idea.
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.0
how did you know what f and g were..? do you just assume?
 one year ago

yakeyglee Group TitleBest ResponseYou've already chosen the best response.1
They were the equations you were given (\(f\) is the upper bound and \(g\) is the lower bound). Does that make sense?
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.0
what defines an upper and lower bound?
 one year ago

NoelGreco Group TitleBest ResponseYou've already chosen the best response.0
I think you want the DIFFERENCE between the two functions in the integrand.
 one year ago

yakeyglee Group TitleBest ResponseYou've already chosen the best response.1
@NoelGreco, I do. Look at the integral again. @monroe17, the upper bound is the function that defines the top part of the bounded area, and the lower bound defines the lower part of the bounded area (look at their positions in the picture you drew).
 one year ago

NoelGreco Group TitleBest ResponseYou've already chosen the best response.0
I looked at both. You have the sum, not the difference.
 one year ago

NoelGreco Group TitleBest ResponseYou've already chosen the best response.0
Just make sure you get \[\frac{ 9\Pi }{ 10 }\]
 one year ago

yakeyglee Group TitleBest ResponseYou've already chosen the best response.1
That is what I meant. \[V=2\pi \int_\color{red}{0}^\color{red}{1} x (3 \sqrt x \color{red}{} 3x^2) dx.\]
 one year ago
See more questions >>>
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.