Please to solve this problem step by step.

Thank you

Monte Carlo Method Assume that f (x) is continuous and strictly increasing on [1, 4] with f (1) = 1 and f (4) = 3. Let g(y) : [1,3] > [1,4] be the inverse of f(x) on [1,4]. (Note: g(y) is also continuous and increasing on [1, 3] and as such integrable on [1, 3].) Monte Carlo Method: Assume that a random number generator is used to generate pairs of numbers (z, y) where 1 g a: S 4 and 0 S y S 3. Suppose that 10,000 such pairs are generated and 9025 pairs are such that for the given (1;, y) we have y 5 f (:3) Use this to estimate f: f (t) dt and briey explain how you came up with your estimate