MAT135 Unit 6: Area (Integration)
5.1 HOW DO WE MEASURE DISTANCE TRAVELED?
Visualizing Distance on the Velocity Graph: Area Under Curve
Positive and Negative Velocity
Change in Position Versus Total Distance Traveled
Left and Right Sums
Accuracy of Estimates
Visualizing Distance on the Velocity Graph: Area Under Curve
Positive and Negative Velocity
Change in Position Versus Total Distance Traveled
Left and Right Sums
Accuracy of Estimates
5.2 THE DEFINITE INTEGRAL
Sigma Notation
Taking the Limit to Obtain the Definite Integral
Computing a Definite Integral
The Definite Integral as an Area
When f(x) Is Not Positive
More General Riemann Sums
Sigma Notation
Taking the Limit to Obtain the Definite Integral
Computing a Definite Integral
The Definite Integral as an Area
When f(x) Is Not Positive
More General Riemann Sums
5.3 THE FUNDAMENTAL THEOREM AND INTERPRETATIONS
The Notation and Units for the Definite Integral
The Fundamental Theorem of Calculus
The Definite Integral of a Rate of Change: Applications of the Fundamental Theorem
Calculating Definite Integrals: Computational Use of the Fundamental Theorem
The Notation and Units for the Definite Integral
The Fundamental Theorem of Calculus
The Definite Integral of a Rate of Change: Applications of the Fundamental Theorem
Calculating Definite Integrals: Computational Use of the Fundamental Theorem