# Area between curves

1. Jan 5, 2004

### tandoorichicken

I need to find the area between y=x and y=x^2
So this is what I did:
$$A = \int (x^2-x) \,dx$$
Then I found the limits of integration x=0 and x=1 because thats where the two graphs intersect
$$A = \int^1_0 (x^2-x) \,dx$$
I ended up with an answer of -1/6
What did I do wrong?

2. Jan 5, 2004

### ShawnD

intersect points:
$$x^2 = x$$

$$x^2 - x = 0$$

$$(x)(x-1) = 0$$

$$x = 1, x = 0$$

The upper limit is the line $$y = x$$, the lower limit is $$y = x^2$$

$$A = \int^1_0 x \,dx - \int^1_0 x^2 \,dx$$

$$A = \frac{x^2}{2} |^1_0 - \frac{x^3}{3} |^1_0$$

$$A = \frac{1^2}{2} - \frac{1^3}{3}$$

$$A = \frac{1}{2} - \frac{1}{3}$$

$$A = \frac{1}{6}$$

3. Jan 5, 2004

### Hurkyl

Staff Emeritus
Which one's bigger?

4. Jan 5, 2004

### tandoorichicken

oh...... I get it