Topic 31 = Stewart 5.2 The Definite Integral = AP Classroom 6.1, 6.2, and 6.3

Lesson Summary: Taking the Area Problem to the Limit!

In general: When we approximate the area under a curve, we are adding up a finite number of rectangles (or trapezoids) on an interval $LaTeX: \left[a,\:b\right]$ . $LaTeX: \lim_{n\longrightarrow\infty}\sum f\left(x\right)\Delta x\:=\:\int f\left(x\right)dx$

Today we're going to tackle some heavy duty Algebra, then you get to switch to the short cuts tomorrow. But you need to be exposed to the mathematics (mathemagics) behind integration at least once! The AP test has never tested on the "long way" to do integration, but you need to have seen it. I will go through this example of taking an integral by hand "the long way" in class, but if you want to review it yourself, here are my notes.

Action Items:

1. Take notes in class. If absent, review the summary above, the powerpoints below and/or the extra resources, take notes as necessary (use the Notes document if you prefer), and make note of any questions you may have.

2. Book Practice: 5.2.2: p. 383 #21-25 odd; and 29.

3. Highly recommended: watch and annotate the AP Classroom videos for 6.1 and 6.2.

Resources:

Topic 31: Riemann Sums & the Definite Integral
Topic 31: Riemann Sums & the Definite Integral Notes (Optional)
AP Classroom Daily Videos: 6.1, 6.2, and 6.3
Stewart, Chapter 5, Section 2
Homework Solutions