A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 one year ago
Find the volume formed by rotating the region enclosed by:
y=x^2, x=y^2 about the line x=5
 one year ago
Find the volume formed by rotating the region enclosed by: y=x^2, x=y^2 about the line x=5

This Question is Closed

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Find the points of intersection. This will also be your integral limits with this lovely region.

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1\(x^{2} = \sqrt{x}\)  Solve!

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Perfect. Now, decide disks or shells. With this wellbehaved region, it really doesn't much matter. Just pick one.

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Disks it is, then. \(\pi\int\limits_{0}^{1} OuterRadius^{2}  InnerRadius^{2} d(Height)\) The "Height" is the xdirection, so we have: \(\pi\int\limits_{0}^{1} OuterRadius^{2}  InnerRadius^{2} dx\) Now indentify that inner and outer radii. What say you?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Well, I would prefer the more literal (5x^2), but it will do since we are just going to square it. Is that the inner or the outer radius?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1No worries. x^2 is the inner radius. Are we calling that 'r'? What is the outer radius, "R"?

monroe17
 one year ago
Best ResponseYou've already chosen the best response.0isn't (5x^2) the outer radius? and yes

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1No, \(x^{2}\) and \(\sqrt{x}\) are a little funny on [0,1] \(\sqrt{x} \ge x^2\;for\;x\in[0,1]\)

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1r is \((5  x^{2})\) R is \((5  \sqrt{x})\) That's all. Did you draw a picture? You will see it at a glance.

monroe17
 one year ago
Best ResponseYou've already chosen the best response.0I'm still confused toward the sqrt(x) where'd that come from?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1x = y^2 ==> y = sqrt(x) We have integration "dx", so we need the representation in terms of x.

monroe17
 one year ago
Best ResponseYou've already chosen the best response.0got it ;p lol just had to see the steps..

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Well, there you have it. Let's see what you get.

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1THAT is the right answer. Good work! Wading through it is FUN, isn't it?!

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Once we realized what the region was, and where the square root came from, you were all over it. This is encouraging! Move on to the next one!
Ask your own question
Ask a QuestionFind 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.