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Find the volume between two intersecting cylinders x^2+y^2=r^2 and y^2+z^2=r^2 using polar coordinates and double integrals only.
 one year ago
 one year ago
Find the volume between two intersecting cylinders x^2+y^2=r^2 and y^2+z^2=r^2 using polar coordinates and double integrals only.
 one year ago
 one year ago

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TuringTestBest ResponseYou've already chosen the best response.1
dw:1352144686186:dw
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
in the xyplanedw:1352144919394:dw\[\sqrt{r^2y^2}\le x\le\sqrt{r^2y^2}\]in the yzplanedw:1352145089843:dw\[\sqrt{r^2y^2}\le z\le\sqrt{r^2y^2}\]leaving\[r\le y\le r\]hm...
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
in the xzplane the intersection is square with sides=2rdw:1352145471598:dw
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
I think the integral is\[\iint\limits_Dr\sin\theta dA=\int_0^{2\pi}\int_0^r r^2\sin\theta drd\theta\]can you check somewhow?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
actually it would have to be\[\iint\limits_Dr\sin\theta dA=2\int_0^\pi\int_0^r r^2\sin\theta drd\theta\]to avoid getting zero
 one year ago

math1234Best ResponseYou've already chosen the best response.0
But the integrand should be r^2 * cos(theta) ?
 one year ago

math1234Best ResponseYou've already chosen the best response.0
since i am integrating z = sqrt(z^2y^2)
 one year ago

math1234Best ResponseYou've already chosen the best response.0
so in polar i thought it was sqrt(r^2y^2) = x = rcos(theta)
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
yeah I just came to that conclusion as well
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
I guess I was right the first time
 one year ago

math1234Best ResponseYou've already chosen the best response.0
but if I integrate with rcos(theta), I end up with zero in the end
 one year ago

math1234Best ResponseYou've already chosen the best response.0
I will get sin(2*pi)  sin(0) = 0.
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
Hm.. now I am not sure again. No way to check I presume...
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
@mahmit2012 double integral help
 one year ago
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