Develop a VBA program that can determine numerically integra

Develop a VBA program that can determine numerically integral of
any given set of data points using
a. Combination of Trapezoidal rule and Simpson’s rule.

Solution

Answer:-

Numerically Integral :-

There are two primary ways to perform numerical integration.

1) Integration of Tabular Data
2) Integration using VBA

1. Integration of Tabular Data :

This type of numerical integration is largely reserved for experimental data.

It is useful for when you want to see how some integral of the experimental data progresses over time.

2. Integration using VBA :

This method works best when you want to integrate an equation with a larger number of integration points and only want to return a single value.

It can be set up with a user defined function (UDF).

Numerical Integration Methods :

Whether you choose to integrate tabular data in the spreadsheet or an equation in VBA, there are two general approximations that are used to estimate the area under the curve.

They are the Midpoint (or Endpoint) Rule and the Trapezoidal rule.

Midpoint Rule :

The midpoint rule estimates the area under the curve as a series of pure rectangles (centered on the data point).

As you can imagine, this results in poor accuracy when the integrand is changing rapidly.

It’s best not to use this method if the number of integration points is limited.

Trapezoidal Rule :

The trapezoidal rule estimates the area under the curve as a series of trapezoids.

This greatly increases the accuracy, regardless of the change in the integrand.

As the number of integration points increase, the results from these methods will converge.