# Area between curves

1. Jan 13, 2004

### 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?

2. Jan 13, 2004

### ShawnD

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

intercepts:

$$y^2 - y^3 = 0$$

$$y^2(1 - y) = 0$$

y = 0, y = 1

integration:

$$A = \int^1_0 y^2 - y^3 dy$$

$$A = \frac{y^3}{3} - \frac{y^4}{4} |^1_0$$

$$A = \frac{1^3}{3} - \frac{1^4}{4}$$

$$A = \frac{1}{3} - \frac{1}{4}$$

$$A = \frac{1}{12}$$