(* problem 11 [5 points] use map to write a function thattakes an int list and an int and multiplies everyentry in the list by the int. you may define auxiliary functions that arecalled by the times_x function. if you defineauxiliary functions, do not use the samename with any pre-declared function inthis homework. *)(* auxiliary functions (if defined) start here *)(* auxiliary functions (if defined) end here *)let times_x (x: int) (lst: int list) : int list =(* your code start here *)[-1](* your code end here *); ; (* test case: all results should be true *)(times_x 5 [1; 2; 3]) = [5; 10; 15]; ; (times_x 5 []) = []; ; (times_x 2 [1; 2; 3]) = [2; 4; 6]; ; in ocaml