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Q8. (a) Given:

ds/dt = 6t²+t^-3 and s = 4 when t = 1

(i) Express s as a function of t. (6)

(ii) Determine s when t = 5. (2)

(b) Calculate the area enclosed by the function y = 8 – 5sin x, the x axis and the ordinates x = 0.5 and x = 2. (Note: angle x is in radians) (8)