Calculating Definite Integrals in R
Overview
In R, you can use the integrate() function to calculate definite integrals. For example,
Code
To calculate $\displaystyle \int_{0}^{3} \left( x^2 + 4x + 1 \right) dx$ and $\displaystyle \int_{0}^{\infty} e^{-x} dx$, you can use the following. Notably, by including inf in the integration interval, it is possible to perform improper integrals as well.
f<-function(x) {x^2 + 4*x + 1}
g<-function(x) {exp(-x)}
integrate(f,0,3)
integrate(g,0,Inf)
Upon actual calculation,
$$ \int_{0}^{3} \left( x^2 + 4x + 1 \right) dx = \left[ {{1} \over {3}} x^{3} + 2 x^2 + x \right]_{x=0}^{3} = 9 + 18 + 3 = 30 $$
and
$$ \int_{0}^{\infty} e^{-x} dx = \left[ - e^{-x} \right]_{x = 0}^{\infty} = 0 - (-1) = 1 $$
can be confirmed.