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Math Help - Double Integral Question

  1. #1
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    Double Integral Question

    This example is from MIT OCW, Multivariable Calculus (http://ocw.mit.edu/courses/mathemati...C_notes_25.pdf)

    Double Integral Question-ex.png

    Shouldn't the highlighted integral start from a, and not zero?
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  2. #2
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    Re: Double Integral Question

    In polar coordinates, when a point is represented as (r, \theta), r is always the distance from the origin to that point. Here, integrating in polar coordinates, as \theta goes from 0 to \pi/4, the corresponding r integral is from the origin to the point where the ray at angle \theta crosses the boundary.
    Last edited by HallsofIvy; July 16th 2014 at 09:45 AM.
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  3. #3
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    Re: Double Integral Question

    At the origin (which is part of R), the distance to the origin is zero. The point on the edge of the square is a distance of a\sec \theta from the origin. So, the integral should start from zero and go to a\sec \theta. As \theta changes, it represents a different line segment of points in that triangle. The first line segment is from the origin along the x-axis to the edge of the square. The last one is the hypotenuse of the triangle.
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  4. #4
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    Re: Double Integral Question

    I got that. Thank you very much both of you.
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