# R code to integrate h() using hit-or-miss method


ex1.fcn <- function(x){
h <- 4/(1 + x^2)
return(h)
}

# my.x <- seq(0,1,length=50)
# plot(my.x,ex1.fcn(my.x),type='l')

my.n <- 1000

my.a <- 0; my.b <- 1
my.c <- 4

my.rand.x <- runif(my.n, min=my.a, max=my.b)
my.rand.y <- runif(my.n, min=0, max=my.c)


my.m <- sum(my.rand.y < ex1.fcn(my.rand.x))

I.approx <- my.c*(my.b - my.a)*(my.m/my.n)

print(I.approx)