How to solve this integral in R? - r

Question

I need to find evaluate the following function, including an integral, in R:
Probability density functions involving multiple variables, where u = t - y.
The problem I'm running into is that while the input variables of the function as a whole are x and t, the integral needs to be evaluated over the variable u = t - y. The functions f and m' both return values, but I don't know how to make it so that R evaluates the integral over this u rather than x or T.
I currently have the following, but this doesn't return the values I'm supposed to be getting, so I'm wondering if I did it properly?
Thank you in advance!
a = 3
b = 10
T = 2.6
mprime = function(x){
return (1/x)
}
f = function(x){
if (a <= x & x <= b){
return (1/(b-a))
}
else{
return (0)
}
}
toIntegrate = function(u){
return (f(u + x)*mprime(T-u))
}
solution = function (x, T){
return (f(T + x)) + (integrate(toIntegrate(T-y), 0, T))
}
solution(5,T)

Answer 1

There are a few errors in your code:
f and other functions you'll be using in your integration need to be vectorised, i.e. it should take a vector as an input and return a vector as an output.
toIntegrate uses x which is neither a global variable nor an argument.
return is a function, so only the expression between parentheses are returned. As a result, your integral would not be evaluated because your function would return f(T+x)
The first argument to integrate should be toIntegrate, not toIntegrate(T-y)
mprime will return infinity for u=t, so the limits may need to be adjusted.
a = 3
b = 10
t = 2.6
mprime = function(x){
return (1/x)
}
f = function(x){
ifelse(a <= x & x <= b,1/(b-a),0)
}
toIntegrate = function(u,x,t){
return (f(u + x)*mprime(t-u))
}
solution = function (x, t){
return(f(t + x) + integrate(toIntegrate, 0, t,x=x,t=t,stop.on.error = F)$value)
}
solution(5,T)