 Course Type AP
 Subject Science and Mathematics
 Level Introductory
 Length 13 Weeks
 Effort 510 Hours/Week
 Institution MITx
About This Course
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.
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.
1. Modeling the Integral
 Differentials and Antiderivatives
 Differential Equations
 Separation of Variables
2. Theory of Integration
 Mean Value Theorem
 Definition of the Integral and the First Fundamental Theorem
 Second Fundamental Theorem
3. Applications
 Areas and Volumes
 Average Value and Probability
 Arc Length and Surface Area
4. Techniques of Integration
 Numerical Integration
 Trigonometric Powers, Trig Substitutions, Completing the Square
 Partial Fractions, Integration by Parts
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.
Instructors

David Jerison
Professor of Mathematics
MIT 
Gigliola Staffilani

Jen French

Karene Chu