Mathematics 9709 · AS & A Level · Numerical solution of equations

Numerical solution of equations — practice question

The diagram presents the curve $y = x - 2\ln x$ together with its minimum point $M$.
(i)[2]

Determine the $x$-coordinate of $M$.

(ii)[3]

Apply the trapezium rule with three intervals to estimate $\int_{2}^{5} (x - 2\ln x)\,dx$, and give your answer correct to 2 decimal places.

(iii)[1]

State, with a reason, whether the trapezium rule gives an under-estimate or an over-estimate for the true value of the integral in part (ii).

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct derivative found

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