Discover the integral---what it is and how to compute it. See how to use calculus to model real world phenomena. Part 2 of 3. How long should the handle of your spoon be so that your fingers do not burn while mixing chocolate fondue? Can you find a shape that has finite volume, but infinite surface area? How does the weight of the rider change the trajectory of a zip line ride? These and many other questions can be answered by harnessing the power of the integral.
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But what is an integral? You will learn to interpret it geometrically as an area under a graph, and discover its connection to the derivative. You will encounter functions that you cannot integrate without a computer and develop a big bag of tricks to attack the functions that you can integrate by hand. The integral is vital in engineering design, scientific analysis, probability and statistics. You will use integrals to find centers of mass, the stress on a beam during construction, the power exerted by a motor, and the distance traveled by a rocket.
This course is part of the Single Variable Calculus XSeries Program.
This course, in combination with Part 1, covers the AP Calculus AB curriculum.
This course, in combination with Parts 1 and 3, covers the AP Calculus BC curriculum.
This course was funded in part by the Wertheimer Fund.
What you'll learn:
- Some differential equation models for physical phenomena and solutions
- The geometric interpretation, and physical meaning of the integral
- The connection of the integral to the derivative
- Several methods of numerically and symbolically integrating functions
- To apply integrals to solve real world problems
Syllabus
Abridged Syllabus
Limits
- Limit Laws
- Continuity
- Intermediate Value Theorem
Differentiation
- Introducing the Derivative
- Rules for differentiation of all known functions
- Approximations
Applications of Differentiation
- Curve Sketching
- Optimization
- Related Rates
