8.5 Area Between Curves (in y)

Right minus left

When the curves are naturally functions of y, integrate ∫[c to d] (x_right − x_left) dy — the curve with the larger x is 'right.'

Choosing dx or dy

The limits are the y-values of the intersections. Choose dx vs. dy based on which makes the region easier to describe.

Key terms

Area between curves (y)

∫[c to d] (x_right − x_left) dy.

Right

The curve with the larger x-value.

Bounds

y-values of the intersections.

When to use dy

When curves are functions of y.

Choice

Pick dx or dy for the easier region.

Try an AP-style question

What is the area between x = y² and x = 4?

1. 16/3
2. 8
3. 64/3
4. 32/3