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Area between curves

  1. Jan 13, 2004 #1
    Find the area bounded by the y-axis and the curve x = y^2 - y^3
    What exactly does the graph of x = y^2 - y^3 look like? And how do you set up the integration?
     
  2. jcsd
  3. Jan 13, 2004 #2

    ShawnD

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    Science Advisor

    Interchange the x and y, does it look familiar now? Rotate that by 90 degrees and you'll get the picture.

    intercepts:

    [tex]y^2 - y^3 = 0[/tex]

    [tex]y^2(1 - y) = 0[/tex]

    y = 0, y = 1

    integration:

    [tex]A = \int^1_0 y^2 - y^3 dy[/tex]

    [tex]A = \frac{y^3}{3} - \frac{y^4}{4} |^1_0[/tex]

    [tex]A = \frac{1^3}{3} - \frac{1^4}{4}[/tex]

    [tex]A = \frac{1}{3} - \frac{1}{4}[/tex]

    [tex]A = \frac{1}{12}[/tex]

    That's my answer anyway.
     
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