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:

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

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

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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.

8 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$value # [1] 12933.33
  my_function ＜- function(x) { out ＜- 2 * x + x^2 + 5 * x^3 } x <- integrate(my_function, lower = 0, upper = 10) x$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