MIDTERM 1 REVIEW TOPICS

Review homework, quizzes, examples from book and lecture examples. Do a couple of sample midterms.
Have integral/differentiation formulas & trig. functions special values in your notes.

4.10 Antiderivatives:

• What they are, how to find them (review differentiation formulas and Chain Rule)
• Most general antiderivative versus specific antiderivative subject to initial condition(s).
• Rectilinear motion & Falling body problems.

5.1 Areas under curves:

• Geometrically and via Riemann Sums.
• Approximations L_n, R_n , M_n.

5.2 The definite integral

• Understand Riemann sums and definition of definite integrals in terms of them
• Distance when the velocity is positive

5.3 FTC I and II

• Know and UNDERSTAND what each of the two theorems are saying.
• Understand the precise relationship between integrals and derivatives
• Know how to do FTC I and II problems, including those involving the chain rule or switching of bounds, or those worded in terms of slopes, concavity, or tangent lines.

5.4 Indefinite Integrals and Net Change

• Familiarize yourself with the table of integral formulas on page 406
• Lots of practice (examples from the text, or among 5.4. pbls 5-40, or sample midterms)
• Understand relation between the net change and the definite integral of the rate of change & specifically distance versus displacement.

5.5 Substitution

• Understand the method and when it is useful.
• Do lots of practice problems: examples in book, from class, and exercises at the end of section (among problems 7-66), or from sample midterms.

6.1 Areas between curves

• How to compute (understand formulas on pages 438 and 440).
• Look over book examples and homework problems.

6.2 Volumes

• Understand how to apply the definition of volume in terms of integral of the area.
• Understand Disks and Washers:

Ø general formula, (Disks) or (Washers).

Ø How to slice and in which variable to integrate, depending on the situation

Ø How to compute R (and r if necessary) in terms of the variable of integration

6.3 Volumes by shells

Ø When to use?

Ø Understand the general formula

Ø How to slice and in which variable to integrate, depending on the situation.

Ø How to compute r and h in terms of the variable of integration.