Integral Calculus
A brief introduction to integral calculus
How do you find the area under a curve? What about the length of any curve? Is there a way to make sense out of the idea of adding infinitely many infinitely small things? Integral calculus gives us the tools to answer these questions and many more. Surprisingly, these questions are related to the derivative, and in some sense, the answer to each one is the opposite of the derivative.
Content
1. Integrals
In this topic, we are going to connect the two big ideas in Calculus: Instantaneous rate and area under a curve. We'll see that a definite integral can be thought of as an infinite sum of infinitely small things and how this connects to the derivative of a function.

2. Integration techniques
We know that a definite integral can represent area and we've seen how this is connected to the idea of an antiderivative through the Fundamental Theorem of Calculus. Unfortunately, integrals aren't always easy to compute. Now, we'll build out our toolkit for evaluating integrals, both definite and indefinite!

3. Integration applications
Let's now use our significant arsenal of integration techniques to tackles a wide variety of problems that can be solved through integration!

4. Sequences, series, and function approximation
Now that we understand what a sequence is, we're going to think about what happens to the terms of a sequence at infinity (do they approach 0, a finite value, or + infinity?).

5. AP Calculus practice questions
Sample questions from the A.P. Calculus AB and BC exams (both multiple choice and free answer).
