9758/2019/P2/Q01

You are given that $I=\int x(1-x)^{\frac{1}{2}} \mathrm{~d} x$
(i) Use integration by parts to find an expression for $I$.

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(ii) Use the substitution $u^2=1-x$ to find another expression for $I$.

[2]

(iii) Show algebraically that your answers to parts (i) and (ii) differ by a constant.

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