Class Info
- Date: Wed Oct 25
- Meeting Info: 10a-11:40a, N719
Announcements
WebWork:
- finish “Integration – Partial Fractions” (extended to Mon Oct 30)
- work on “Applications – Areas Between Curves” (due Wed Nov 1)
Topics
We went through some examples of computing “areas between curves” from the WebWork. This the first of some applications of integration we will study:
Here is the example we set up in class Monday:
As illustrated above, the general strategy involves identifying which curve (i.e., function) is “the top boundary” of the area and which is the “bottom boundary.” And in many examples (such as the one above) we have to solve for where the curves intersect, in order to figure out the endpoints of the interval of integration:
Here is a more complicated example we set up in class (Problem 3 on the WebWork). The two curves intersect at 3 points, with which curve is on top switching at the middle point. So we need to set up two separate integrals for the total area enclosed:
We also discussed an example (Problem 5) where it is more convenient to integrate with respect to y:
Here is the video I posted in the previous Class Recap:
And here is a followup video showing an example of integrating with respect to y:
