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