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Q8. (a) The shape of a rugby ball may be represented by the rotation of the shaded area in Fig Q8(a), about the x axis, through one complete revolution.

(i) Determine, using integral calculus, a formula for the volume of a rugby ball in terms of the constants A and B.       (10)

(ii) Use the result in Q8(a)(i) to calculate the volume of an adult size rugby ball which has a = 15 cm and b = 9.8 cm.(2)

(b) Evaluate: ∫₀^π/6(2sinθ/tanθ) dθ. (4)