Chapter 4.2 - Area

Objectives:

• • Use sigma notation to write and evaluate a sum.

  • Understand the concept of area.

  • Approximate the area of a plane region.

  • Find the area of a plane region using limits.

Summations (for Day #33 lesson)

Getting familiar with the properties of summation notation (i.e. what you are and are not allowed to do with sigmas). Also utilize the basic summation formulas to evaluate more complicated summations.

Here's my working of "Example 4" from the textbook, showing how to use limits and sigma to compute the upper/lower/left/right sum of a curve. Maybe (or maybe not) handed out in class.

Area pt1 (for Day #36 lesson)

Using summations to approximate the area under a curve, and then using limits to determine the exact area.

(FYI This video was recorded months earlier than most of the others, so that's why it looks a bit different).

Here's the "Part 1" assignment handout, with intervals that start at x=0.

Relationship between Left/Right/Upper/Lower sums (image)

Area pt2 (for Day #36 lesson)

Another exercise using summations and limits to determine the exact area under a curve. This time, the interval doesn't start at x=0.

Here's the "Part 2" assignment handout, with intervals that do not start at x=0.

Format/Topics of Chapter 4.2 Assessment (unused this year)

15 Multiple Choice

• All topics are fair game, as usual

6 Short Answer

• General Solutions vs. Particular Solutions, Initial Conditions

• Particular Solutions for s(t), v(t), a(t)

• Write a sum in sigma notation

• Calculate a sum in sigma notation

• Formula for sum of n terms, fully simplified to A + B/(Cn) + D/(En^2)

• Area of a planar region

Format/Topics for Q2 Exam through Ch. 4.2

20 MC Questions (50% of score)

• • Everything 'til now is fair game

7 Free Response (50% of score)

• • Derivatives (Ugly Algebra)

  • Related Rates

  • MVT, Rolle's, IVT, EVT

  • Increasing/decreasing intervals, Extrema tests, Concavity intervals, Inflection points

  • Interpreting an f' graph

  • Optimization

  • Limits at infinity

  • Antiderivatives (aka Indefinite Integration)

  • Particular Solutions to a differential equation, including Position/Velocity/Acceleration situations

  • Area under a curve using limits & summation formulas on interval [a, b], both for a=0 and a≠0.

Your study guide consists of completed homework assignments, the most recent test, and the Barron's AP preparation book given to you at the beginning of the year.