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Homework Help: Multivariable Intergration

  1. Jul 15, 2012 #1
    Find the volume of the region inside both the sphere x^2+y^2+z^2= 4 and the cylinder (x-1)+y^2=1

    using cylindrical coordinates.

    I was thinking the inner limits would go from +(2-r) to - (2-r)
    the middle intervals would go from 0 to 1
    and the outer limits 0 to 2pi

    is my approach correct
  2. jcsd
  3. Jul 16, 2012 #2


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    1. Did you mean the cylinder ##(x-1)^2 + y^2 = 1\, ##? I am assuming so.
    2. You have to tell us what your order of integration is. For example are you describing the limits for ##dzdrd\theta\, ##?
    3.If so, notice that ##\sqrt{4-r^2}\ne 2-r##
    4. To get correct ##r,\theta## limits you need to find the polar equation of the cylinder and plot its trace in the xy plane. Your limits are wrong.
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