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Math Help - Integration Areas Problem

  1. #1
    sjg
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    Integration Areas Problem

    Trying to do a problem that involves the space bounded by y=x^2, y=x^4, y=16 and x=5. Above the x-axis in the positive x and y directions.
    Need to find the area by integrating with respect to y. I am getting an answer but almost certain it isn't right, getting thrown off by the fact the area isn't bounded by the x-axis (y=0). Any help?
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  2. #2
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    Re: Integration Areas Problem

    Notice that the area under given conditions is nothing but the area bounded between the curves y = x^2 and y = x^4 in the first quadrant.
    For this we will find the points of intersection of the two curves. that is got by solving the two equations and we get the x coordinates of their points of intersection as
    0 and 1.
    So the required area would be area under the curve y = x^2 - area under the curve y = x^4 from 0 and 1
    = integral from 0 to 1 x^2 dx - integral from 0 to 1 x^4 = 2/15
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