1. Albus Dumbledore loves you all! Integration Terms

2. What is an integral?

3. The integral is the opposite of the derivative and is sometimes referred to as the “antiderivative”. It represents the displacement between a function and the xaxis. On this graph it represents the combined area of the rectangles (called Riemann sums) as the number of rectangles approaches ∞

4. Definite Integral

5. When the Integral has certain, defined boundaries. You can tell when an integral is defined by its notation:

6. Indefinite Integral

7. When the integral has no set boundaries. Because the integral is based on the displacement of the entire function, every solution to an indefinite integral problem must be followed by +C

8. Substitution

9. In many Integral problems, you’ll have to substitute. We usually use the variable u to substitute in. For this problem, we would set u=x+2 and derive it, du=1dx. We can now take put u in for x+2 in the problem:

10. What’s this position, velocity, and acceleration nonsense all about?

11. Ho HoHo! Such spirit in you, Harry! Well, velocity is the derivative of position, and acceleration is the derivative of velocity (or second derivative of position). In terms of integrals, the integral of velocity is equal to the original position of the function.

12. Eliminating the Constant

13. When we are asked to find the position of a function from a given velocity, we need another piece of information: a point on the original function. When we know that f(0)=1, we can plug in 0 for x and solve for the C value, or constant.