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Math Help - Area between two curves

  1. #1
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    Area between two curves

    I know that the formula for area between curves is the anti derivative of f(x)-f(g), however i'm unsure of how to take the anti-derivative of the absolute value, please help!


    determine the area between the curves |x| and -2x^2 + 5
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    Quote Originally Posted by Lupus7874 View Post
    I know that the formula for area between curves is the anti derivative of f(x)-f(g), however i'm unsure of how to take the anti-derivative of the absolute value, please help!


    determine the area between the curves |x| and -2x^2 + 5
    You should know that |x| = x for x > 0 and |x| = -x for x < 0. From the graph that you drew (and I know you've drawn a graph because your teacher would have taught you that drawing a graph is the very, very first thing that you're meant to do) it should be clear that, by symmetry, the required area is:

    2 \int_0^a (-2x^2 + 5) - x \, dx

    where a is the positive x-coordinate of the intersection point of y = -2x^2 + 5 and y = x (one of your jobs is to get the value of a).
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