If we have a function which is well-defined for some , its integral over those two values is defined as This is called a definite integral, and represents the area under the graph of in the region between and , as shown in the figure below. The function is called the integrand, and the two points and are called the bounds of the integral. The interval between the two bounds is divided into segments, of length each. Each term in the sum represents the area of a rectangle, and as , the sum converges to the area under the curve.
Figure
A multiple integral involves integration over more than one variable. For instance, when we have a function that depends on two independent variables, and , we can perform a double integral by integrating over one variable first, then the other variable:
