R: Integration using R integrate() function

This post demonstrates the usage of a numerical integration function in R, integrate(), accompanied by an example featuring a slope factor-related term.

Numerical Integration in R

Given a slope factor-related term as the integrand, an analytical solution exists.

R code

The supplied R code executes numerical integration via the integrate() function in R, while additionally showcasing analytical integration through the closed-form expression for the given problem.

#--------------------------------  # Integrand #--------------------------------  f_int <- function(t, T, la) {     return(-(1-exp(-la*(T-t)))/la) }   #-------------------------    # comparison #-------------------------    T = 4; t = 1; tau = T-t; la = 1.2   print("Two Integrations")   cat("Numerical solution:\n"); (1/(T-t))*integrate(f_int, lower = t,                      upper=T, T=T, la=la)$value   cat("Analytical solution:\n"); (1/la)*(1-exp(-(la*(T-t))))/(la*(T-t)) - 1/la   Colored by Color Scripter

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The output confirms the equivalence of results from both integration methods. Hence, in cases where no analytical expression is available, numerical integration can serve as a reliable alternative.

>  [1] "Two Integrations" >  Numerical solution: > (1/(T-t))*integrate(f_int, lower = t, upper=T, T=T, la=la)$value [1] -0.6081768 >  Analytical solution: > (1/la)*(1-exp(-(la*(T-t))))/(la*(T-t)) - 1/la [1] -0.6081768 >  Colored by Color Scripter

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