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
Example Sigma Notations
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].
Example Is a partition of [0, 10]. the largest of all the subinterval widths subinterval widths Riemann Sum
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
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
Step 1 Step 2 Step 3 Riemann Sum
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]. Find Riemann sum Example partition the interval [0,1] into n equal subintervals Riemann Sum
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 of ƒ over [a, b] Remark: the definite integral of ƒ over [a, b] The Definite Integral
Notation: the definite integral of ƒ over [a, b] Remark: The Definite Integral
Remark: The Definite Integral
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
Example: Evaluate the following integrals by interpreting each in terms of areas. The Definite Integral
THE DEFINITE INTEGRAL Term-103
Property (1) THE DEFINITE INTEGRAL Example:
THE DEFINITE INTEGRAL Property (2)
THE DEFINITE INTEGRAL Property (3)
THE DEFINITE INTEGRAL Term-091
EXAM-1 TERM-102 The Definite Integral
THE DEFINITE INTEGRAL Term-092
THE DEFINITE INTEGRAL
Term-092
THE DEFINITE INTEGRAL Term-082
Term-092
Term-082
THE DEFINITE INTEGRAL Term-103
DEFINITION