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!

Double integral over a region

  1. Apr 12, 2015 #1
    1. The problem statement, all variables and given/known data
    [itex]\iint\limits_D x{\rm{d}}x{\rm{d}}y[/itex] where [itex]x = \sqrt{2y - y^2}, y = \sqrt{2x - x^2}[/itex]

    2. Relevant equations


    3. The attempt at a solution
    I have figured out the region in question:
    jlC2Xbj.png
    But how do I get the limits of integration?

    Ah, perhaps..
    [tex]\int_0^1 \int_{1-\sqrt{1-y^2}}^{\sqrt{2y-y^2}} x {\rm{d}}x{\rm{d}}y[/tex]
    In the inner integral I consider what X is bound by and then the 2nd integration would be just from 0 to 1 since that's what y is bound by. Not really worried about the actual calculation itself, but the most challenging bit is figuring out the bounds.
     

    Attached Files:

    Last edited: Apr 12, 2015
  2. jcsd
  3. Apr 12, 2015 #2

    BruceW

    User Avatar
    Homework Helper

    yep. those bounds look good. I get the same ones at least :)

    edit: you could also do the integration in the opposite order (i.e. dy first), but I think that way is more time-consuming. and of course, in that method, the limits would look similar, but would have x instead of y.
     
    Last edited: Apr 12, 2015
  4. Apr 12, 2015 #3

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    @nuuskur: Of course, if you were "worried" about evaluating the integral, it would be wise to convert the equations to polar coordinates and set it up and work it that way.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Double integral over a region
Loading...