1. Not finding help here? Sign up for a free 30min 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 integrals: cartesian to polar coordinates

  1. Nov 27, 2015 #1
    1. The problem statement, all variables and given/known data
    Change the Cartesian integral into an equivalent polar integral and then evaluate.

    2. Relevant equations
    x=rcosθ
    y=rsinθ

    upload_2015-11-27_1-53-51.png
    I have:
    ∫∫r2cosθ dr dθ

    The bounds for theta would be from π/4 to π/2, but what would the bounds for r be?

    I only need help figuring out the bounds, not with the evaluating.

    The answer for the problem is 36 (or so says the back of the textbook).
     
  2. jcsd
  3. Nov 27, 2015 #2

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    The area of integration forms a right triangle subtending angle from 45 to 90 degree, so the limit for r would be a function of ##\theta##. For a hint, as you sweep the triangle in between those two limiting angles, the projection ##r \sin \theta## is constant.
     
  4. Nov 27, 2015 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    For every theta, a line from the origin, making angle theta with the y-axis, to the line y= 6 is the hypotenuse of a right triangle with one leg of length 6. [itex]cos(\theta)= \frac{6}{h}[/itex].
     
  5. Nov 30, 2015 #4
    Thank you both!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted