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Math Help - Double Integration

  1. #1
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    Double Integration

    I am just learning about double and triple integration, but I am stuck on this problem:

    Find the average distance to the x-axis for points in the region bounded by the x-axis and the graph y = x - x^2

    I am not quite sure how to set up the double integral. I appreciate the help.
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  2. #2
    MHF Contributor

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    The "distance to the x-axis" for any point (x, y) is, of course, y.

    To find the average value of function f(x,y) over two-dimensional region U, take the integral of f(x,y) over that region, divided by the area of the region:
    \frac{\int_U f(x,y) dxdy}{\int_U dxdy}.

    Here, you region is "bounded by the x-axis and the graph "y= x- x^2[/tex]". If draw a graph you will see that that graph is a parabola that intersects the x-axis at x= 0 and x= 1. In order to cover that region, you will have to take x going from 0 to 1 and, [b]for each x, y from 0 to x- x^2.

    You want \frac{\int_{x=0}^1\int_{y= 0}^{x- x^2} y dy dx}{\int_{x=0}^1\int_{y=0}^{x- x^2} dy dx}.
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