Advanced Placement Calculus
Syllabus: Chapter 5
D. Kramer add page numbers for problems
Day,
Date
Wed
10/30
Thurs
10/31
Text Section
Terms & Concepts
5-1
Class Work
5-2 Differential
x  dx , y  dy
p. 194
#2,5,6,12,28,
30,36,42
Ch. 4 Test
y  f ( x  x)  f ( x )
dy  l ( x  x)  l ( x)  f '( x)dx
p. 194 Q
WS 5-3 First
Column
5-3
Antiderivative, Indefinite Integral
 Definition
 Notation
 Integrand, Operator
Constants, Sums, Differences
Products
WS 5-3
p. 202
#1,5,9,11,15,
17,19,23,29,
33
5-4
Riemann Sums
Notes
p. 210 #4
p. 209
#1,9,10,11,13
Riemann Sum
Program
Use program
for only #13.
error  y  dy
Fri
11/1
Mon
11/4
Practice
Problems
p. 189
#1-6
p. 194
#1,3,7,9,
15,25,27,31
Partition, subinterval, Rn 
p. 202 #8,10,14,
20,26,32,37
#41
#13,36
(for #36,
prove that it is
correct)
p. 202 Q
#8
n
 f (c )x
k 1
k
k
Left, Right, Midpt, Upper, Lower
Definite Integral
b

Written
Assignment
None
f ( x)dx  lim x 0 Rn if this limit exists
Exact value of
integral #14,15
a
Tues
11/5
Integrability
 if continuous then integrable
 if bounded with finite number of
discontinuities, then integrable
p. 209Q
5-5
Mean Value Theorem
p. 217 #6,10
Begin
WS Good Probs 5-6
(2 sides)
Rolle’s Theorem
Wed
11/6
5-6
Fundamental Theorem of Calculus
 FTOC
 Integral versus Area
 Exact value of an integral using the
limit of a sum.
1. Find a formula for Ak
2. Find the limit of the sum of
Ak
p. 217
#1,2,5,9,11,
29,32
#14,15,16
Practice
Problems 5-6
in packet
Written
Assignment 5-6
in packet
p. 217 Q
Exact Value Problem

6
0
(3 x  x 2 )dx
Practice Problems
Finish
WS Good Probs 5-6
p. 225 Q
Thurs
11/7
Fri
11/8
5-7
Properties of the Definite Integral
 negative integrands
 adding with same integrand
 switching bounds a & b
 symmetric functions – even/odd
 sums and differences, constants
Review
Numerical Integration
 Trapezoid Program
 Riemann Program
 MATH #9 fnInt(function,x,a,b)
 CALC #7 f ( x)dx
p. 232
#14,18,
32,34,36,37,38
p. 231 Q
p. 232
#15,19,
21,23,25,27,
29,31,33,35
(graphs in
packet)
#5,11,17
Steno
p. 226
#1,3,7,9
p. 226 # 2
Exact Values for Integrals
 Algebraic: limit of sum
 Fundamental Theorem
Review
Jeopardy
None
Test 5-1 through5-7
Test
Optional p.260
# R1, R2, R3
R5bcd, R6bcd
None
5-8
Area Between Curves
Horizontal & Vertical Slices
y  x2 , y  6  x
1
x  6  y2 , x  y2
2

Mon
11/11
Tues
11/12
Wed
11/13
Thurs
11/14
Fri
11/15
5-9
Volume of Solids of Revolution
 Solids of revolution
5-9, Supplement
Volume of Known
Cross-Sectional Solids
Mon
11/18
5-11 Review
Tues
11/19
Mon
11/25
Test 5-1 through 5-11
5-10
(Skip Simpson’s rule)
Group Quiz: AP Problems
p. 238
#4,6,8,16, 22,29
p. 236 Q
p. 247
#2,6,8,10,12
p. 247 Q
Worksheet
p. 256 #10
Steno
p. 265
#T13, T16, T17
Test
p. 255 Q
Group Quiz
p. 237
#1,7,13,
15,25,28
p. 246
#1,3,7,9,11
p. 246 #16,18,
19,20,22,25
Answers:
16. 0.289
18. 8.378
20. 7.55
22. 1.597
(optional)
p. 262
#R7, R8, R9
None
#19,21
#4 (Sketch
the graph.)
Answer: 30.6
#21
Note – the
region is along
the y-axis.
Sketch the
graph.
None
p. 269 #1-4
None
p256# 7,12,19
(Note for
#19: Clear
out any xvalues in table
before doing
this problem)
#8 (Sketch
the graph.)