Topic 38 Area Between Curves = Stewart 6.1 Area Between Curves = AP Classroom 8.4, 8.5, and 8.6: Area Between Curves

Lesson Summary: we have been finding the area between curves every time we have evaluated an integral -- it is just that the "second curve" in each case has been the line y = 0. Now we are extending the idea of area between curves to any two curves.

In general,

if integrating with respect to x, use upper minus lower
if integrating with respect to y, use right minus left.
working by hand requires
- finding intersections (set functions equal to each other and solve)
- knowing which function is above and which below (or right and left) and where; and
- re-writing to solve for x, if you are working with two curves that are not "above/below" each other;
if allowed, the graphing calculator is handy to
- find points of intersection (for the limits of integration); and
- use absolute value to bypass the need to know which function is "on top."

Action Items:

1. Take notes in class. If absent, review the summary above, the powerpoints below and/or the extra resources, take notes as necessary (use the Notes document if you prefer), and make note of any questions you may have.

2. HW: 6.1.1: #1, 3; 7-11 odd; 15, 18, 22.

3. WaMap Assignment (Optional) 4.5, Area Between Curves

4. Highly recommended: watch and annotate the AP Classroom videos, 8.4, 8.5, and 8.6.

Resources: