Download presentation
Presentation is loading. Please wait.
1
Sigma Notations Example This tells us to start with k=1 This tells us to end with k=100 This tells us to add. Formula
2
Example Sigma Notations
3
Riemann Sum is called a partition of [a, b]. Example Is a partition of [0, 10]. Is a partition of [0, 9]. Is a partition of [0, 10].
![Riemann Sum is called a partition of [a, b]. Example Is a partition of [0, 10].](http://images.slideplayer.com./27/9003474/slides/slide_3.jpg "Is a partition of [0, 9]. Is a partition of [0, 10]..")
4
Example Is a partition of [0, 10]. the largest of all the subinterval widths subinterval widths Riemann Sum
![Example Is a partition of [0, 10].](http://images.slideplayer.com./27/9003474/slides/slide_4.jpg "the largest of all the subinterval widths subinterval widths Riemann Sum.")
5
Riemann sum for ƒ on the interval [a, b]. Find Riemann sum Example Riemann Sum
![Riemann sum for ƒ on the interval [a, b]. Find Riemann sum Example Riemann Sum](http://images.slideplayer.com./27/9003474/slides/slide_5.jpg "Riemann sum for ƒ on the interval [a, b]. Find Riemann sum Example Riemann Sum")
6
Riemann sum for ƒ on the interval [a, b]. Find Riemann sum Example Riemann Sum
![Riemann sum for ƒ on the interval [a, b]. Find Riemann sum Example Riemann Sum](http://images.slideplayer.com./27/9003474/slides/slide_6.jpg "Riemann sum for ƒ on the interval [a, b]. Find Riemann sum Example Riemann Sum")
7
We start by subdividing the interval [a,b] into n subintervals The width of the interval [a,b] is b-a the width of each subinterval is The subintervals are Riemann Sum
![We start by subdividing the interval [a,b] into n subintervals The width of the interval [a,b] is b-a the width of each subinterval is The subintervals are Riemann Sum](http://images.slideplayer.com./27/9003474/slides/slide_7.jpg "We start by subdividing the interval [a,b] into n subintervals The width of the interval [a,b] is b-a the width of each subinterval is The subintervals are Riemann Sum")
8
Step 1 Step 2 Step 3 Riemann Sum
9
Riemann sum for ƒ on the interval [a, b]. Find Riemann sum Example partition the interval [0,1] into n equal subintervals Riemann Sum
![Riemann sum for ƒ on the interval [a, b].](http://images.slideplayer.com./27/9003474/slides/slide_9.jpg "Find Riemann sum Example partition the interval [0,1] into n equal subintervals Riemann Sum.")
10
Riemann sum for ƒ on the interval [a, b]. Find Riemann sum Example partition the interval [0,1] into n equal subintervals Riemann Sum
![Riemann sum for ƒ on the interval [a, b].](http://images.slideplayer.com./27/9003474/slides/slide_10.jpg "Find Riemann sum Example partition the interval [0,1] into n equal subintervals Riemann Sum.")
11
Definition: The Definite Integral the definite integral of ƒ over [a, b] Example the definite integral of ƒ over [0, 1] Find
![Definition: The Definite Integral the definite integral of ƒ over [a, b] Example the definite integral of ƒ over [0, 1] Find](http://images.slideplayer.com./27/9003474/slides/slide_11.jpg "Definition: The Definite Integral the definite integral of ƒ over [a, b] Example the definite integral of ƒ over [0, 1] Find")
12
Definition: the definite integral of ƒ over [a, b] Remark: the definite integral of ƒ over [a, b] The Definite Integral
![Definition: the definite integral of ƒ over [a, b] Remark: the definite integral of ƒ over [a, b] The Definite Integral](http://images.slideplayer.com./27/9003474/slides/slide_12.jpg "Definition: the definite integral of ƒ over [a, b] Remark: the definite integral of ƒ over [a, b] The Definite Integral")
13
Notation: the definite integral of ƒ over [a, b] Remark: The Definite Integral
![Notation: the definite integral of ƒ over [a, b] Remark: The Definite Integral](http://images.slideplayer.com./27/9003474/slides/slide_13.jpg "Notation: the definite integral of ƒ over [a, b] Remark: The Definite Integral")
14
Remark: The Definite Integral
15
Area under the curve the definite integral of f from a to b If you are asked to find one of them choose the easiest one. The Definite Integral
16
Example: Evaluate the following integrals by interpreting each in terms of areas. The Definite Integral
17
THE DEFINITE INTEGRAL Term-103
18
Property (1) THE DEFINITE INTEGRAL Example:
19
THE DEFINITE INTEGRAL Property (2)
20
THE DEFINITE INTEGRAL Property (3)
22
THE DEFINITE INTEGRAL Term-091
24
EXAM-1 TERM-102 The Definite Integral
25
THE DEFINITE INTEGRAL Term-092
26
THE DEFINITE INTEGRAL
27
Term-092
28
THE DEFINITE INTEGRAL Term-082
29
Term-092
30
Term-082
31
THE DEFINITE INTEGRAL Term-103
32
DEFINITION
Similar presentations
![Aim: Riemann Sums & Definite Integrals Course: Calculus Do Now: Aim: What are Riemann Sums? Approximate the area under the curve y = 4 – x 2 for [-1, 1]](/24/7261222/big_thumb.jpg "Aim: Riemann Sums & Definite Integrals Course: Calculus Do Now: Aim: What are Riemann Sums? Approximate the area under the curve y = 4 – x 2 for [-1, 1]>")
