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 2 years ago
Find the volume formed by rotating the region enclosed by:
y=x^2, x=y^2 about the line x=5
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1\(x^{2} = \sqrt{x}\)  Solve!

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

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

tkhunny
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0got it ;p lol just had to see the steps..

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

tkhunny
 2 years 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
 2 years 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!
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