For many functions it is impossible to find a primtive function and therefore it is impossible to use the fundamental theorem of calculus to solve the integral.

Luckily there are ways to cope with such circumstances with the aid of numerical methods. Here one has deviced a formula for approximation of the integral.

The perhaps the simplest one is the trapezoidal formula.

The principle is to divide the area into well-known entities( in this case trapezoids) for which the area may readily be computed.

A more refined method is thee.

 Simpson’s rule. This can be viewed as a combination of the midpoint-rule and the trapezoidrule. The midpoint rule basically amounts to approximating the area by rectangles.