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Q8. (a) The average value, y̅, of a function y = f (x) in the range x = a to x = b is given by:

y̅ = 1/(b-a) ∫^b_af (x)dx

Determine the average value of the function y = 5x⁴ -4x in the range x = 0 to x = 2. (6)

(b) Fig Q8(b) shows a sketch of the function y = 3x² -x³

Calculate the volume of the solid of revolution obtained when the shaded area is rotated once about the x axis. (10)