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Area between curves

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?
 

ShawnD

Science Advisor
658
1
Originally posted by tandoorichicken
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?
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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