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: Supposedly simple double integral

  1. Nov 3, 2007 #1
    double integral of xy dA
    in the triangular region of (0,0), (3,0), (0,1).
    my problem that I am having is finding the limits I am suposed to find dx or dy in. I figure I should use 0 to 3 for dx, but then i do dy from 0 to what? Help appreciated.
  2. jcsd
  3. Nov 3, 2007 #2


    User Avatar
    Science Advisor

    Try drawing a picture of the region. Then, for a given value of x, what values of y lie within the region? This gives you the limits of integration for y, given x. (Of course, you must then do the y integral before you do the x integral.)
  4. Nov 3, 2007 #3
    so then the parameters for y would be: 0 to x/3?
  5. Nov 4, 2007 #4


    User Avatar
    Science Advisor

    Yes, because the upper boundary is the line y= x/3.

    It is a very good exercise to "swap" the limits of integration. Suppose you wanted to integrate with respect to x first and then y? Clearly to cover the entire triangle, you must take y going from 0 to 1. For each y, then, x must go from the left boundary, x= 0, to the "right" boundary which is still that line y= x/3. That is, x must go from x= 0 to x= what? Do the integral of xy both ways and see if you get the same thing.
  6. Nov 4, 2007 #5
    still not getting the right answer.

    I used the parameters dy= 0 to 1 and dx= 0 to -3y+3 and got 2.375.
    the answer was wrong.
    I did it the other way with dy=0 to x/3+1 and dx= 0 to 3 and got another wrong answer.
    what am I doing wrong?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook