Category: Class Agendas (Page 5 of 9)

Class Info

• Date: Mon Oct 23
• Meeting Info: 10a-11:40a, N719

Announcements

WebWork:

• finish “Integration – Integration by Parts” (extended to Mon Oct 30)
• work on “Area Between Curves”

Topics

We went through one more examples from the WebWork “Integration – Partial Fractions”–a longer more challenging exercise, given that it involves “an irreducible quadratic factor” in the denominator (i.e., a quadratic that can’t be factored further–in this case “x^2 + 9”:

For such a factor, we have to use a linear factor numerator (“Bx+C”) above, and we have to use the “method of equating coefficients” to solve for B and C (since there’s no x-values which make the irreducible quadratic factor 0!):

The last steps, in order to integrate is to split up the numerator over the quadratic factor into two separate terms:

We can solve the first two integrals. But for the last integral–the constant over x^2+9–we need the following “inverse trig” integral:

We mentioned that you can also study Example 3.33 Sec 3.4 of the textbook, which involves the (simpler) irreducible quadratic factor x^2+1:

We finished the class by starting to look at how to set up definite integrals to calculate “areas between curves”:

Here is a video with some similar examples:

Class Info

• Date: Mon Oct 16 & Wed Oct 18
• Meeting Info: 10a-11:40a, N719

Announcements

WebWork:

• finish “Integration – Integration by Parts” (due Mon Oct 23)
• work on “Integration – Partial Fractions” (due Wed Oct 25)

Office hours: Friday 11a-12p on Blackboard Collaborate.

Topics

We spent most of the class period on Monday reviewing Exam #1. We then introduced the next topics–integration by the “method of partial fractions” and computing “the area between two curves.” We spent Wednesday going through examples from the WebWork “Integration – Partial Fractions”.

From Monday:

From Wednesday:

The method of partial fractions is covered in Sec 3.4 of the textbook. You can also watch the examples in these PatrickJMT videos: