ABSTRACT
This chapter discusses several methods for calculating numerical integrals. It also discusses advantages and disadvantages of each method by comparing their algorithmic errors. The chapter considers one-dimensional and multidimensional integrals and potential pitfalls during their calculations. The ability to calculate integrals is quite important. The chapter also considers the evaluation of a one-dimensional integral, also called quadrature, since this operation is equivalent to finding the area under the curve of a given function. It analyzes how the Monte Carlo method outshines all others for the case of multidimensional integration. Riemann's definition gives us directions for the rectangle method: approximate the area under the curve by a set of boxes or rectangles. The approximation of each interval with a trapezoid is an attempt to circumvent the weakness of the rectangle method.
