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.

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.

This course was funded in part by the Wertheimer Fund.

Learn more about our High School and AP* Exam Preparation Courses

Calculus 1A: Differentiation

Calculus 1C: Coordinate Systems & Infinite Series

*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.

Quantum physics? In this three-part series, theoretical physicist Brian Greene helps you understand its origins and its impact on today’s world. Part 1. “Uncovering a New Reality” Theoretical physicist and best-selling author Brian Greene takes us on a journey through the discoveries of quantum physics. How is it that Newtonian mechanics gave way to the…

Amazing, Life Changing Tutor
Before I met Jonathan, I was struggling through most of my STEM classes because I was simply not studying properly. He taught me all kinds of new study habits that would help me to save time, raise my grades, and lower my stress. Jonathan was specifically tutoring me in vector calculus and is an amazing tutor on the subject. You will walk away from a lesson with a game plan knowing exactly what you need to do before your next session with him or before your next exam in order to do well in the course. I highly recommend him as a tutor.

This calculus video tutorial shows you how to find the indefinite integral of functions such as xlnx, xe^2x, xcosx, x^2 e^x, x^2 lnx, e^x cosx using the integration by parts formula. Some problems require the use of the equation two or three times. This video contains plenty of notes, examples, and practice problems for you…

Four worked-out examples demonstrating two techniques (primarily using logic) for determining where the shading goes, when graphing a linear inequality. The first technique is the “test point” method, which is explained here, but only shown once. The “logic” method is preferable because you don’t need to use any arithmetic or pick any points, you just…

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