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Homework Help: 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

    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


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    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


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    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!
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