Let h(x)=sinx+x be defined on [0,π].
(i) Calculate the average value of h on the sub-interval [0,2π].
(ii) Calculate the average value of h on the sub-interval [2π,π].
(iii) Without performing any further integration, identify which of the two averages found in parts (i) and (ii) is larger and justify your answer briefly.
(iv) Determine the ratio of the larger average to the smaller one, writing your answer in simplest form.