Chapter 13: The Integral in Calculus
Day
1
2
Subject Matter of the Day
 Lesson 13.1 From the Discrete to the Continuous
o d = vt
o Interval: x or t
o Area under the curve =  of little areas
o A = l*w
o A bh
o Atrap = (b1 + b2)h
 Problems
Page Examples
1 15
788
4, 7
 Lesson 13.2 Riemann Sums
o Riemann Sum: Estimate of the area under a curve
o
Intermediate pt.
interval
o Constant Interval:
o
o b – largest a – smallest n – # of intervals
o Right End Point vs. Left End Point
o Calculator: Right End Point:
o (equation, variable, lower, upper)
o Riemann Sum:
o
o
3
((equation with (x*x) instead *x),variable, lower, upper)
(+) or (-) starting point from x*x
 Problems
Page Examples
1 24
795
1,
 Lesson 13.3 The Definite Integral
o Upper Riemann Sum: right end point
o Lower Riemann Sum: left end point
 n decreases by 1 so, 1 (n – 1)
o Integral Notation:

 a & b are the end points of the interval
 dx is in terms of the independent variable
 Read as: The integral from a to b of …
o Aka:
smallest x possible
o Gives the exact value
o Also can be found using Area
 Lines: use area formula of trapezoid or triangle
 Parabolas: us area formula of circle
 Problems
Page Examples
1 21
802
4, 8, 11
4
 Ms 13.1 to 13.3
 Lesson 13.4 Properties of the Definite Integral
o
+
=
o
5
o
=
o
 Problems
1 18
6
–
=
Page
809
+
= c*
Examples
5, 8
 Work Day
 Lesson 13.5 The Area Under a Parabola
o If a > 0 then

=

=

7
=

= cb – ca
o
 Problems
1 24
8
9
=
Page
816
Examples
8, 9
 Ms 13.4 to 13.5
 Lesson 13.6 Volumes of Surfaces of Revolutions
o Vsphere =
o Vcylinder = r2h
o Vcone =
o Vprism = lwh
o
o Volume for region bound by function:
o
o Circle: x2 + y2 = r2
 Problems
Page Examples
1 19
823
4, 7, 9
goes to sphere
10
 Lesson 13.7 The Fundamental Theorem of Calculus???? Extra
11
 Ms 13.6 to 13.7
12

Chapter 13 Review
13

Test Chapter 13
Final Exam:
1
 Review Book Quizzes Chapter 11,6, & 7
2
 Review Book Quizzes Chapter 8 & 9