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

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

Letâ€™s do thisâ€¦

## 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 ï¼œ 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, donâ€™t hesitate to let me know in the comments section.

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

• Hey Gearoid,

Please have a look at the modified example code below:

```my_function ï¼œ- function(x) {
out ï¼œ- 2 * x + x^2 + 5 * x^3
}

x <- integrate(my_function,
lower = 0,
upper = 10)
x\$value
# [1] 12933.33```

Regards,
Joachim

• Thank you, Joachim.

• Hi Gearoid,

Thank you for the kind comment, glad it helped!

Regards,
Joachim

• Thank you so much, it helped me too

• Hi Sarv,

Thank you very much for the kind words, glad you liked our tutorial!

Regards,
Matthias

• How would you make the function for unknown bounds/limits

• Hi Theo,

It is possible to assign Inf (i.e. infinite) to the lower and upper arguments.

Regards,
Joachim

• 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

• 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