5. (5 marks) The water level of a restricted tidal basin is modeled with the function h(t)sin²(t) + ½ where one tidal cycle passes every 2 time units. Two modification to the model are proposed: 1. a correction function g(t) = ½ cos(2t) and 2. The addition of a function to account for development of a standing wave in the basin, ƒ(t) = cos(t)³ sin(t) + 1.= (a) Calculate the average water level predicted from the original function over one tidal cycle. \frac{1}{2 \pi} \int_{0}^{2 \pi} h(t) d t (b) Calculate the average water level predicted from the addition of the correction function to the original function over one tidal cycle, \frac{1}{2 \pi} \int_{0}^{2 \pi}(h(t)+g(t)) d t (c) Calculate the average water level predicted from the addition of the standing wave function, \frac{1}{2 \pi} \int_{0}^{2 \pi} f(t) h(t) d t