Warmup 10/2
On sticky notes write
Sticky notes (1) & (2): Two things you learned from
yesterday.
Sticky note (3) : One thing you are still confuse or
unsure about.
Rules
n
1.
n
 c  cn
c a
2.
k 1

k
k 1
n
c  ak
k 1
n( n  1)
3.  k  1  2  3  ...  n 
2
k 1
n
n(n  1)(2n  1)
4.  k  1  2  3  ...  n 
6
k 1
n
2
5.  k 3  13  23  33  ...  n3   n( n  1) 
 2 
k 1
n
2
n
6.
a
k 1
k
2
 bk 
2
2
n
a
k 1
k

2
n
b
k 1
k
Area  lim  left sum 
n
n 1
Area  lim x  f ( xi 1 )
n 
i 1
Area  lim  right sum 
n
n
Area  lim x  f  xi 
n 
i 1
n


Area  lim  x f (ci ) 
n 
 i 1

ci
- Either the left or right sum.
ci  a1  (i  1)(x)
ci  a1  i(x)
Section 4.2
Be seated before the bell rings
DESK
homework
Warm-up (in
your notes)
Agenda :
go over hw
Notes lesson 4.4
Notebook
Learning Target
Table of content
13) Extreme Values
14) Role’s Thm
MVT
1
Page
1
19)4.4 Fundamental
15) Increasing/Decreasing & 1st deriv. Test
16) Concavity and 2nd deri. Test
17) Optimization
Theorem of Calculus
18) 4.2/4.3 Area
19)4.4 FTC
HW:p.288;5-33
odd,35-38
4.4. Fundamental Theorem of Calculus
Fundamental Theorem of Calculus:
Example 1:

3
1
3
3
3
3
x
(3)
(1)
2
| 
x dx 

3 1
3
3
26
1
9 

3
3
The following guidelines can help you understand the use
of the Fundamental Theorem of Calculus.
1. Provided that you can find the antiderivative of f, you now have
a way to evaluate a definite integral without having to use the
limit of a sum
2. The notation show is convenient
3. It is not necessary to included a constant of integration C
More Example – Evaluating a Definite Integral
Evaluate each definite integral.
Example 1 – Solution
Example of absolute functions :
Another example of splitting up definite integrals
More examples
1
−1
1
𝑑𝑥 =
2
𝑥