## Double Integration

# Single Integration

In single integration, we essentially added all of the y-values for every x-value in a set domain. Back then, the definition of an integral on [a,b] was the limit of a Riemann sum:

# Inner Partitions

In double integration, we do something where we split a region up into many squares, and we sum up the volumes of the prisms made from the squares. Now, we add up all of the z-values for every square created by the point (x,y).

To actually calculate a double integral, the area of the partitions approaches zero.

# Evaluation

Before we start, we have to define the two types of regions.

## Type 1

This is "normal", or at least more familiar. This is when the y's are bound by two functions f(x) and g(x) and the x's are bound between constants.

## Type 2

This is inverted. This means the x's are bound by two functions f(y) and g(y), and the y's are bound between constants.