8.4 Area Between Curves (in x)

Top minus bottom

The area between an upper curve f and a lower curve g from a to b is ∫[a to b] (f(x) − g(x)) dx — always top minus bottom, so the integrand is nonnegative.

Finding bounds

The limits a and b are usually the intersection points; find them by setting the two functions equal.

Key terms

Area between curves (x)

∫[a to b] (top − bottom) dx.

Top

The upper curve.

Bounds

Usually the intersection points.

Find intersections

Set the functions equal.

Integrand

Nonnegative (top − bottom).

Try an AP-style question

What is the area between y = x and y = x² on [0, 1]?

1. 5/6
2. 1/6
3. 1/3
4. 1/2