Write R code for the following Question:
a. Use the Monte Carlo method with n = 100 and n = 1000 to estimate integral top=1 bottom=0 cos(2πx) dx. Compare the estimates to the exact answer.
b. Use Monte Carlo to evaluate integral top=1 bottom=0 cos(2πx 2) dx. Can you find the exact answer?
Thus far I have:
#Estimation of f=integral(cos(2piX)dx) from x=0,1
#generate random values from appropriate ranges
x<-data.frame(x=runif(n,min=0,max=1)
#evaluate at f
f=integral(cos(2(pi)X)dx)
#Approximate by averaging with appropriate scaling
(1/16)*(1)*(3/32)*mean(f)