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Help w/ double integration to solve common volume of two intersecting cylinders

  1. Apr 10, 2004 #1
    Hi I am taking MV calc and a paticular question in the double integrals chapter asks to find the volume bounded by x^2 + y^2 = r^2 and y^2 +
    z^2 = r^2. I already know what the shape looks like (Steinmatic solid) and also know the answer can be achieved using single integration as well, but here I am having difficulty visualizing the integrand for a D. Integral--- the limits of integration will definetely involve constants of r. What would be your suggestion for setting up the integral? The shape is identical on all sides and symmetical--- could there be a way to solve one region and multiply the answer to get the volume, or something along those lines?

    Thanks for your help.
  2. jcsd
  3. Apr 10, 2004 #2

    matt grime

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    The integrand is 1. What the limits are is more interesting. do it in the order, what dx then dy then dz

    x from 0 to sqrt(r^2-y^2),

    y from 0 to sqrt(r^2-z^2)

    z from 0 to r

    multiply that answer by 8

    That sound right to everyone else?
  4. Apr 10, 2004 #3
    Multiplying by 8 makes total sense!!! Thanks i ended up getting (16/3)*r^3 exactly what it should be! Thanks.
  5. Feb 21, 2010 #4
    how would u write it if it were a double integral not triple?
  6. Feb 21, 2010 #5


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