Definition of numerical integration

1. What is meant by numerical integration?
2. What is difference between integration and numerical integration?
3. What is the basic meaning of integration?
4. What are the method used in numerical integration?

What is meant by numerical integration?

Numerical integration methods can generally be described as combining evaluations of the integrand to get an approximation to the integral. The integrand is evaluated at a finite set of points called integration points and a weighted sum of these values is used to approximate the integral.

What is difference between integration and numerical integration?

Ordinary integration is usually done with pencil and paper and it requires analytical functions. In numerical integration, the functions don't even need to be functions. They are just strings of numbers and it is all done by computer.

What is the basic meaning of integration?

In Maths, integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions into parts.

What are the method used in numerical integration?

There are a few basic methods of numerical integration, differing in a way of approximation: midpoint rule, • trapezoidal rule, • Simpson's rule. In all of them we get approximated value of integral, but they are determined with various errors and speed of convergence to the correct result.