Calculus AB - Unit Three
The Integral and the Fundamental Theorem of Calculus
Integrals are used in a wide variety of practical and theoretical applications. AP Calculus students should understand the definition of a definite integral involving a Riemann sum, be able to approximate a definite integral using different methods, and be able to compute definite integrals using geometry. They should be familiar with basic techniques of integration and properties of integrals. The interpretation of a definite integral is an important skill, and students should be familiar with area, volume, and motion applications, as well as with the use of the definite integral as an accumulation function. It is critical that students grasp the relationship between integration and differentiation as expressed in the Fundamental Theorem of Calculus — a central idea in AP Calculus. Students should be able to work with and analyze functions defined by an integral.
Click on a link to jump ahead to the following sections:
- Unit 1: Introduction to Integrals
- Unit 2: The Definite Integral
- Unit 3: The Fundamental Theorem of Calculus
- Unit 4: Differential Equations
- Unit 5: Applications
- Unit 6: Assessment Tasks
- Supplemental Tasks:
Resources - Integrals
The following are links to resources for Integrals:
The following are other free resources:
- GeoGebra - Free online math tools
- Desmos - Free online graphing calculator
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