Author: Suman Ganguli (Page 5 of 12)

Class Info

• Date: Mon Nov 6
• Meeting Info: 10a-11:40a, N719

Announcements

WebWork:

• “Applications – Volumes of Revolution” (due Friday Nov 9)

Topics

We recapped how to set up integrals for areas between curves, and for volumes of solids of revolution:

We set up an example from the WebWork that that involves calculating a volume using cylindrical shells, and also looked at an example from the textbook (Example 2.15 from Sec 2.3):

We then introduced “improper integrals”–where we integrate over an infinite interval, using a limit:

Class Info

• Date: Wed Nov 1
• Meeting Info: 10a-11:40a, N719

Announcements

WebWork:

• “Applications – Areas Between Curves” (due Sun Nov 5)
• “Applications – Volumes of Revolution” (due Friday Nov 9)

We will have a quiz on Monday, with one exercise on integrating using the method of partial fractions and one exercise on computing the area between two curves.

Topics

We went through a few additional examples from the “Volumes of Revolution” WebWork set.

We introduced “the washer method,” which variation on the disk method, also used for calculating the volume of a solid of revolution “by slicing”–but for solids which have a hollow “cavity”, and so the object is sliced into “washers” (disks with an empty inner circle):

Here is a better sketch for that exercise:

And here is an illustration of the general case, and the resulting integral:

See also Example 2.10 from Sec 2.2 of the textbook. We watched parts of this video as well:

We also introduced a different method for calculating the volume of a solid of revolution: the method of “cylindrical shells.”

This is covered in Sec 2.3 of the textbook. Here are the images we looked at:

We set up an example from the WebWork:

Here is a video with more examples using the cylindrical shells method: