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Math Help - plz help area between curves

  1. #1
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    plz help area between curves

    1>find the area bounded by the graph of y=x and y=x^3.Providesketch of the region on axis
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  2. #2
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    Quote Originally Posted by gracy View Post
    1>find the area bounded by the graph of y=x and y=x^3.Providesketch of the region on axis
    Hello, Gracy,

    you have the graphs of 2 functions:
    l(x)=x and
    f(x)=x^3

    The enclosed area is calculated by the difference of these two functions:
    u(x)=l(x)-f(x)=x-x^3

    Calculate the zeros of u. These zeros correspond with the intercepts of l and f. You'll get: x = -1 or x = 0 or x = 1

    For symmetry reasons the area can be calculated as:

    A=2\cdot \int_{0}^{1}\left(x-x^3 \right)dx

    I've got A=0.5

    I've attached a sketch of the enclosed area.

    EB
    Attached Thumbnails Attached Thumbnails plz help area between curves-eingeschl_flaeche1.gif  
    Last edited by earboth; December 8th 2006 at 12:39 PM.
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