Recitation 22

Recitation 22 (The Definite Integral)

Objectives:

• Students will be able to approximate a Riemann sum and identify if their sum is an over or under estimate.

Important Notes:

• [ (5 minutes)] Welcome the class to recitation. Ask students if they have filled in the notes section of the packet. Tell students that they should be filling in the notes section before coming to recitation.

• [ (20 minutes)] Have students do problem 1. This is a long problem and the goal in part f is to get them to develop a midpoint or average rule.

• [ (10 minutes)] Have students work through problem 2. Students often struggle to see the shapes in a problem like this.

• [ (15 minutes)] Have students work through problem 3. Don't let students take antiderivatives!

• [ (15 minutes)] Have students work through problem 4. It looks like something involving the gridlines has not printed correctly. Make sure to reprint these off and bring them to recitation with you.

• [ (10 minutes)] Have students work through problem 5.

• [ (5 minutes)] Depending on how class is going you might want to either go over a problem or have students continue working on problems 6, 7, 8 and 9.

*Note: the solution for problem 9 is
abs(\sum\limits_{i=0}^{799} \frac{5}{800} ((2+5/800 i)^2-3)- \sum\limits_{i=1}^{800} \frac{5}{800} ((2+4/800 i)^2-3))=5/800(2^2-3-(7^2-3))=0.251