The study of calculus can be separated into two components: derivative or differential calculus and integral calculus. Integral calculus can be thought of as dealing with the area under curves, but it also touches on two- and three-dimensional situations with path and surface integrals. On the most basic level, with finding the area under curves, integrals can be the reverse of derivatives--hence their other name, anti-derivatives. There are two major types of integrals on the lowest level: the definite and the indefinite. The definite integral provides a numerical range over which the integral is to be calculated; the indefinite integral is looking for a closed-form solution to which any range can be applied.

Integral calculus is often used in conjunction with differential equations. A differential equation will, as its name indicates, provide information about the rate of change of a function in its differential form. The...