How to Calculate Integral in Excel

5.1 min read|Last Updated: January 26th, 2024|Categories: excel|

Integral is one of the most important tools in mathematics. It can be used to calculate area, volume, and many other useful parameters. In this blog, we are going to discuss the methods of calculating integrals in Excel.

The Concept of Integral

In calculus mathematics, there are two main operations: integration and differentiation. Integral is the inverse operation of differentiation. Integration is a way of adding slices to find the whole. Its most common use is the calculation of the area under a curve.

There are two types of integrals: definite and indefinite integrals. In an indefinite integral, you must have the function F formula to calculate its integral, which gives F when it’s differentiated. If you want to calculate Integrals with Excel, forget indefinite integral because it’s a matter of analytical calculation.

Definite integral relates to numerical values. It is used in applied mathematics, statistics, science, and many more. It can be calculated using indefinite integral and numerical methods.

Methods of Calculating Integral

When it comes to integration, you may face two situations: you have an equation to integrate or a corresponding x and y values. As we discussed earlier, Excel can not integrate using analytical methods. So, in any case, you will have to turn the equation into numbers.

Based on numerical mathematics, we can calculate an integral via two methods derived based on the calculation of the area of geometric shapes.

Trapezoidal Method for Calculating Integral

This method assumes that the area under a curve consists of several trapezoids. The area of a trapezoid can be calculated using the formula below:

How to calculate the area of a trapezoid" tag

Now, all we have to do is add up the area of these trapezoids to calculate the integral.

Assume that we have a dataset of (x,y) related to each other with the F function.

y=F(x)

F can be any function. To calculate the integral by this method, we add up the area under the curve between all consecutive points.

Example: calculating integral of a function

We are asked to calculate the integral below:

Follow the steps below:

  1. Set the dx value, which is the height of the trapezoids. Let’s call it “h.” and set it 0.1 in this example.
  2. Set x values from 0 to 2 with a step of the desired “h.”
  3. Calculate y values using the function formula.
Turning the function equation into numbers
  1. Type “=0.1/2*(B3+B2)” in cell C3 and press Enter. Then click on the little box in the bottom right corner of the cell and drag it to the last point (cell C22).
  2. Now, add up the area value of all trapezoids using the SUM function.
How to calculate the integral of a function by trapezoidal method

Note: The lower the dx, the more accurate will be the result.

Example: Calculating the area under a curve when the function is not available.

In this example, we want to calculate the area under a curve. As we discussed earlier, integration is the way.

Here, the ∆x is not constant. So we can not