My Math Forum Double Integration with Polar Coordinates

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 April 16th, 2017, 05:58 PM #1 Senior Member   Joined: Jan 2017 From: Toronto Posts: 175 Thanks: 2 Double Integration with Polar Coordinates Find the volume inside both r = 1 and r^2 + z^2 = 4. Answer: 32 * pi/3 - 4 * sqrt(3) * pi This is what I came up but the result is only half of the correct anbswer.. Any tips would be much appreciated. $\int_{0}^{2\pi}\int_{0}^{1} sqrt(4-r^2) r drd\theta$
 April 16th, 2017, 06:21 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 1,944 Thanks: 1011 basically you have a cylinder capped at both ends with a partial sphere $V = \displaystyle 2 \int_0^{2\pi} \int_0^1 \int_0^{\sqrt{3}}~r~ dz ~dr~d\theta + 2 \int_0^{2\pi} \int_0^1 \int_{\sqrt{3}}^{\sqrt{4-r^2}}~r~ dz ~dr~d\theta$
April 17th, 2017, 04:55 PM   #3
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Quote:
 Originally Posted by romsek basically you have a cylinder capped at both ends with a partial sphere $V = \displaystyle 2 \int_0^{2\pi} \int_0^1 \int_0^{\sqrt{3}}~r~ dz ~dr~d\theta + 2 \int_0^{2\pi} \int_0^1 \int_{\sqrt{3}}^{\sqrt{4-r^2}}~r~ dz ~dr~d\theta$
Is there any free online polar coordinates 3D graphing tool?

 April 17th, 2017, 06:02 PM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,165 Thanks: 867 See the responses at your post 3D polar coordinates problem

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