## 4.7 Areas Between Curves

### Summary

Integrals are used to find the area between two curves. An integral formula is developed and its applicability is discussed in a variety of examples.

• The formula for the area between two curves.
• How to use the formula to find the area between two curves.
• How to find the area between two curves that are functions of y.

On-screen applet instructions: The applet depicts the total area between two curves, as well as the net area. In each case an integral formula is given. In the case of total area, explain the role of the absolute value and how it is evaluated over the interval of integration.

### Examples

Find the area of the region bounded by y2 = 2x and x – y = 4. Sketch the region.

Find the area between

and

Sketch the region.

Consider the region between the circles x2 + y2 = a2 and x2 + y2 = b2 in the first quadrant. Divide this region into two pieces with the curve defined by

in the first quadrant. Find the ratio of the two regions created and sketch them.

### Videos

See short videos of worked problems for this section.

### Exercises

See Exercises for 4.7 Areas Between Curves (PDF).

Work online to solve the exercises for this section, or for any other section of the textbook.

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel