Recitation 26

Recitation 26 (The Fundamental Theorem of Calculus Part 2)

Objectives:

• Students will be able to use the FTC part 2.
• Students will be able to solve basic differential equations.

Important Notes:

FTC Part 2 hard problems are really all about the chain rule.

Lesson Plan

• [ (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.

• [ (25 minutes)] Have students work problem 1 through 3.

• [ (25 minutes)] Have students work problems 4, 5, and 6. Many students will get stuck, you should plan a mini lecture explanation to get the class working well together.

\textbf{Example:}

Suppose we want to calculate \[\frac{d}{dx} nt_0^{x^2} \sin(t)dt.\] Let $f(x)= nt_0^x \sin(t)dt.$, then we are actually calculating \[\frac{d}{dx} f(x^2)\] which is $f'(x^2)2x$, therefore, \[\frac{d}{dx} nt_0^{x^2} \sin(t)dt=\sin(x^2)2x.\]

• [ (15 minutes)] Tell students that Problems 6-12 are good practice problems but there is no way there is sufficient time in a recitation to solve all the problems. Have students pick which two they want to solve today and tell them to complete the others in preparation for the coming exam.

• [ (5 minutes)] Solve one of problems 6 through 9 for the class.