Read and Watch 1

16.1.1: Definition of Double Integral over a Rectangular Region (17:59)

16.1.2: Evaluating Double Integrals with Iterated Integrals with Example (15:41)

16.1.5: Average Value of a Function of Two Variables (04:28)

16.2.1: Types of Regions (12:33)

Read and Watch 2

16.2.5: Example Switching the Limits of Integration (10:05)

16.2.6: Volume between Two Surfaces with Example (15:14)

16.3.1: Double Integrals over Polar Rectangles (18:11)

16.3.2: Double Integrals over Polar Rectangles Example 1 (07:03)

16.3.3: Volume between two Polar Surfaces Example 2 (08:26)

16.3.4: Double Integrals over Polar Rectangles Example 3 (06:39)

16.3.5: Double Integrals over General Polar Regions (15:20)

16.3.6: Finding Area of a General Polar Region Example 5 (06:53)

Practice

Use the practice problems at the end Sections 16.1, 16.2, and 16.3 in our text to practice what you've learned this week. The problems generally increase in difficulty in each subsection. The problems towards the end of the section get increasingly more involved, so I recommend working a few problems from each of the earlier subsections, checking your answers against the back of the book, and then venturing as far as you desire.

Review and Reflect

Take a look at the learning objectives for this week (found in the overview above). After completing everything above, assess how well you feel you meet each objective (say, on a scale from 1-5, 1 being the least comfortable and 5 being confident with having met the objective). The idea here is to make a record of how you feel about each objective so that you can easily go back to it before, say, an exam or at the end of the chapter and easily see what topics you should review. It can also be helpful if you are having trouble understanding a concepts later in the course.

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