1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Double integrals for volume

  1. Mar 24, 2009 #1
    1. The problem statement, all variables and given/known data
    find the volume of the solid that lies below the graph of z = 1/(x^2 + y^2) and that is bounded laterally by the cylinder set y =|x| and the planes y = 2 and y = 8

    2. Relevant equations

    3. The attempt at a solution
    well i kno that the z equals equation is what i will be integrating, so i was wondering the significance of the y = planes. If done on an xy plane then the y equals is the bounds and im integrating the region b/w y = 2 and 8 in regards to the y =|x|

    What i set up was the integral from 2 to 8 of the integral of -y to y of (1/x^2 + y^2)dydx

    Am i on the right track?
  2. jcsd
  3. Mar 24, 2009 #2
    Close, but be careful. When you're integrating with respect to y, you also have y in the bounds. You have an expression for how y varies, so use that instead.
  4. Mar 25, 2009 #3


    Staff: Mentor

    The region over which you're integrating is a trapezoid, where the parallel sides are the lines y = 2 and y = 8. The nonparallel sides come from y = |x|. Because the graph of z = 1/(x^2 + y^2) is symmetric with respect to both the x- and y-axis, you can make your integral a little simpler by integrating over half the region and multiplying your result by 2.

    In other words, one possibility for your integral is this:
    2\int_{y = 2}^8 \int_{x = 0}^y <your function> dx dy
    You could set it up so that the order of integration is reversed, but that would make things more complicated.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook