The integrands of many definite integrals are sufficiently complicated that an
antiderivative cannot be found, so their value cannot be determined analytically. In such cases the value of the integral must be determined numerically.
In this section we describe two methods for the numerical integration of a
definite integral. The slightly simpler and far less accurate of the two
methods is called the trapezoidal rule. The second and far more accurate
method, which computationally takes no longer, is called Simpson’s rule.
These are only two of a large class of methods for the numerical integration
of definite integrals which collectively are called quadrature formulas. The
term quadrature formula is simply a synonym for numerical integration formula.