Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Understanding what integrating in polar gives you

  1. Apr 1, 2012 #1
    I am not understanding integration with polar coordinates, or at least visualizing what is happening. Here's the integral calculated in Wolfram:

    http://www.wolframalpha.com/input/?i=integrate+(r^2(cost^2-sint^2))r+drdt+t=(0)..(pi/2)+r=(1)..(2)+

    the integral before I changed it to polar was just ∫R(x2-y2)dA where R is the first quadrant region between the circles of radius 1 and 2

    mathematically it makes sense that the answer is 0.

    but when you draw the picture it is a quarter of a washer in the xy plane. This does not seem like 0 to me. Would someone please explain where my thinking is going wrong?

    Thanks

    First post:smile:
     
  2. jcsd
  3. Apr 1, 2012 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The function x^2 -y^2 is symmetric in that region when you reflect over the line x=y, with the function negative on one half and positive on the other
     
  4. Apr 1, 2012 #3
    ok that makes sense, but why the line x=y?
     
  5. Apr 1, 2012 #4

    chiro

    User Avatar
    Science Advisor

    Think about the nature of ^2 term in terms of the solutions (hint: + and -).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook