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Math Help - area between line and parabola

  1. #1
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    area between line and parabola

    How do you find the area of the region enclosed by the line y=2x+4 and the parabola y=4-x^2 in the xy-plane? Thank you
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  2. #2
    MHF Contributor alexmahone's Avatar
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    The line and the parabola intersect at the points where the x-coordinate is 0 and -2. (Obtained by solving the 2 equations.)

    Area=\int\limits_{-2}^{0}(4-x^2)-(2x+4) dx
    =\int\limits_{-2}^{0} (-x^2 - 2x)dx
    =-\frac{x^3}{3}-x^2 | (from -2 to 0)
    =0-(\frac{8}{3}-4)
    =\frac{4}{3}
    Last edited by alexmahone; June 11th 2009 at 09:17 AM.
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