Integrate Function in R (Example) | Using integrate() to Compute Integral

This tutorial illustrates how to integrate a user-defined function using integrate() in R.

Table of contents:

1) Constructing Example Function

2) Example: Applying integrate() to User-Defined Function

3) Video & Further Resources

4) Subscribe to the Statistics Globe Newsletter

5) Thank you!

Let’s do this…

Constructing Example Function

The following manually defined function is used as basement for this R programming tutorial:

my_function <- function(x) {    # Create own function
  out <- 2 * x + x^2 + 5 * x^3
}

Example: Applying integrate() to User-Defined Function

This Example shows how to compute the integral of a function using the integrate() command of the R programming language. For this, we need to specify the name of our function, a lower limit, and an upper limit:

integrate(my_function,          # Apply integrate in R
          lower = 0,
          upper = 10)
# 12933.33 with absolute error < 1.4e-10

The RStudio console returns the result: 12933.33 with absolute error ＜ 1.4e-10.

Video & Further Resources

I have recently published a video on my YouTube channel, which illustrates the examples of this tutorial. You can find the video below.

In addition, you might want to have a look at the other tutorials of my website. Please find some other articles below.

In this article you learned how to apply the integrate function in R. In case you have any further questions, don’t hesitate to let me know in the comments section.

14 Comments. Leave new

Gearoid
September 24, 2022 11:00 am

Thanks – how do you then extract the value of the integral (12933.33 in the example above) to use in further calculations?

Reply
- Joachim
  September 29, 2022 4:15 pm
  Hey Gearoid,
  
  Please have a look at the modified example code below:
  my_function ＜- function(x) { out ＜- 2 * x + x^2 + 5 * x^3 } x <- integrate(my_function, lower = 0, upper = 10) x$value # [1] 12933.33
  Regards,
  Joachim
  Reply
Gearoid
September 29, 2022 4:24 pm

Thank you, Joachim.

Reply
- Joachim
  September 30, 2022 5:47 pm
  
  Hi Gearoid,
  
  Thank you for the kind comment, glad it helped!
  
  Regards,
  Joachim
  
  Reply
Sarv
October 16, 2022 11:42 am

Thank you so much, it helped me too

Reply
- Matthias (Statistics Globe)
  November 7, 2022 10:52 am
  
  Hi Sarv,
  
  Thank you very much for the kind words, glad you liked our tutorial!
  
  Regards,
  Matthias
  
  Reply
Theo
November 16, 2022 6:20 pm

How would you make the function for unknown bounds/limits

Reply
- Joachim
  November 17, 2022 9:00 am
  
  Hi Theo,
  
  It is possible to assign Inf (i.e. infinite) to the lower and upper arguments.
  
  Regards,
  Joachim
  
  Reply
Vitomir
January 30, 2023 6:21 pm

Hello Joachim,

How can I construct the interval without the x value function inside? I only need an integral of 1/4 between 1 and 9.

Something like —> a <- integrate( 1/4, lower = 1, upper = 9)

Thanks,
Vitomir

Reply
- Cansu (Statistics Globe)
  January 31, 2023 9:53 am
  Hello Vitomir,
  
  I am also not so familiar with the integrate function, but my quick search led me to this solution:
  my_function <- function(x) { # Create own function 1/4 } integrate(Vectorize(my_function),1,9) # 2 with absolute error < 2.2e-14
  See the source here.
  
  Regards,
  Cansu
  Reply
shivshankar nila
July 2, 2024 9:39 am

my_function <- function(x,z) { # Create own function
out <- 2 * x + x^2 + 5 * x^3+z
}

result<-integrate(my_function, # Apply integrate in R
lower = 0,

upper = 10,z=z)
result$value

How do we integrate this kind of integration? Here z is variable and taking value z.

Reply
- Joachim (Statistics Globe)
  July 2, 2024 3:58 pm
  Hey,
  
  Are you looking for something like this?
  my_function <- function(x, z) { out <- 2 * x + x^2 + 5 * x^3 + z return(out) } z <- 1 # Example value for z result <- integrate(function(x) my_function(x, z), lower = 0, upper = 10) result$value
  Regards,
  Joachim
  Reply
shivshankar nila
July 2, 2024 5:07 pm

Thank you for your reply. The aim is to do double integration, as in the sample example below.
First, integrate the function f(x,z)=xz with respect to x from x=z to x=10.
Then, integrate the resulting expression with respect to z from z=0 to z=10.

Reply
- Joachim (Statistics Globe)
  July 5, 2024 6:30 am
  
  Thanks for the clarifications. Unfortunately, I also didn’t find a good solution for this.
  
  I run a Facebook discussion group where people can ask questions about R programming and statistics. Could you post your question there? This way, others can contribute/read as well: https://www.facebook.com/groups/statisticsglobe
  
  Regards,
  Joachim
  
  Reply