The function f(x)=3x+2 is continuous on the interval [1,b], where b>1. Its average value on this interval is 11.
a. (i) Evaluate ∫1bf(x)dx and simplify your result.
b. (ii) Using the result of part (i), form an equation in b corresponding to the given average value.
c. (iii) Solve the equation obtained in part (ii) to determine the value of b.