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Find the volume formed by rotating the region enclosed by:
y=x^2, x=y^2 about the line x=5
 one year ago
 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
 one year ago

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

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

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

tkhunnyBest ResponseYou've already chosen the best response.1
Disks 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?
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.1
Well, 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?
 one year ago

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

monroe17Best ResponseYou've already chosen the best response.0
isn't (5x^2) the outer radius? and yes
 one year ago

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

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

monroe17Best ResponseYou've already chosen the best response.0
I'm still confused toward the sqrt(x) where'd that come from?
 one year ago

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

monroe17Best ResponseYou've already chosen the best response.0
got it ;p lol just had to see the steps..
 one year ago

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

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

tkhunnyBest ResponseYou've already chosen the best response.1
Once 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!
 one year ago
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