Math 191    Study Guide for Hour Quiz #4 on Chapter 5    C.S. Davis

You are responsible for the subject matter in chapter 5 and section 4.10 The following topics are central in their importance. I have assigned a minimal number of exercises at the end of each topic from Calculus, by James Stewart, 6^th ed. . Work more similar exercises if you need to do so in order to master the topics.

4.9.

1.

Given a derivative or differential formula, write the associated integration formula. (for notation)

2.

Find the most general antiderivative of a given function. P279#1,3,5,7,11,15

3.

Solve a simple initial value problem (IVP). (An IVP is a differential equation + initial condition(s)). P279#21,27,33

4.

Sketch the graph of the antiderivative function F, given the graph of the function f and a point on the antiderivative curve. P280#45,46,47

5.

Solve a word problem in which acceleration is given and velocity and position are sought. P280#53,55,57

5.1

1.

Give the names, diagrams and statements describing the two major problems of calculus. (A repeat from the beginning of the term.)

2.

From a graph, table or formula of a function, give a lower estimate and an upper estimate for the area under a curve using a given number of subdivisions. P298#1,3

3.

From a graph, table or formula of a velocity function, give a lower estimate and an upper estimate for the distance traveled by the object for a given number of subdivisions. P299#13,15

4.

Write an expression involving a limit and a sum for the exact area under a given curve. P299#17

5.2

1.

Define the definite integral of a function f from a to b.

2.

From a graph, table or formula of a function defined on a closed interval, find estimates for its definite integral using any of these rules: left endpoint, right endpoint, lower rectangles, upper rectangles and midpoint. P310#5,7,9; P541#1abc

3.

Write the definite integral as a "lim sum" (limit of a summation) and write a "lim sum" as a definite integral. P311#17,29

4.

Use the definition ("lim sum") to evaluate a definite integral. P311#23

5.

Use the graph of simple functions to evaluate definite integrals (and thus to find the area under the curve.) P311#33

6.

Use the properties and the comparison properties of definite integrals. P312#47,49,51,53,55

7.

Distinguish between definite integral in general and area in particular.

5.3

1.

State the Fundamental Theorem of Calculus, part 1 (FTC1) and part 2 (FTC2).

2.

Given a graph or a formula of a function f, use the FTC1 to find the values of g(x) where g(x) = the integral of f(t)dt from 0 to x. P321#3,7,11,15,47,49

3.

Use the FTC2 to evaluate a definite integral. P321#,19,23,27,31

5.4

1.

Evaluate definite integrals using FTC2. P330#19,29,35

2.

Apply the Total Change Theorem to find the following:

a,

displacement as an integral of velocity.

b.

cost as an integral of marginal cost.

c.

total change of a quantity as an integral of its derivative. P330#47,4755,57,63

5.5

1.

Perform integration by the substitution rules (change of variable) P338#1-29 every other odd, P339#35-43 every other odd