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# Chapter 21. Integration of Functions

The task of finding the area enclosed by a given curve is an old problem. The ancient Egyptians, for example, tried to find the area of a circular field by relating it to the area of a square field. The search for a solution to the area problem gave rise to the field of integral calculus, where the integral of a function between two limits is equal to the area under that function. In modern science and engineering, integral equations are widely used to model physical phenomena including things such as aerodynamic analysis and radiation computations.

Integral equations can be divided into two types—proper and improper. A proper integral is one with finite integration limits and whose function can be evaluated ...

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