Multiple integrals are a set of integrals that are taken over more than one variable. In general the more integrals that are taken the higher the dimension of space that is involved in the area's shape. For instance if two integrals comprise a multiple integral then the outcome corresponds to an area, three integrals correspond to a volume. A multiple integral generally appears as: f(x, y, z) dx dy dz. To compute a multiple integral one begins from the most inner integral and evaluates that one first, then proceeds to the next inner integral and so on. In the example above the most inner integral would treat x as the variable whilst y and z are taken as constants. The order in which one carries out computations can be varied but care must be exercised to correctly transform the limits to correspond to the proper...