The quadratic function f(x)=3x2+4x is defined for 1≤x≤4.
a. (i) Calculate the area enclosed between the graph of y=f(x), the x-axis, and the lines x=1 and x=4.
b. (ii) Using your answer to part (i), determine the average (mean) value of f(x) on the interval [1,4]. Express your answer as an exact fraction.