The Fundamental Theorem of Calculus

Recall that the fundamental theorem of calculus basically defines the integral:

$$\int_a^b df = \int_a^b \ddx{f} dx = f(b) - f(a)$$

To put it another way, if $F = \ddx{f}$ :

$$\int_a^b F dx = f(b) - f(a)$$

This justifies referring to integration as ``antidifferentiation'' - differentiation run backwards. Integration consists of finding a function whose derivative is the function being integrated.

As before, what we can do with scalars, we can do with vectors - with bells on, two or three different ways.