Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram gives a sketch of the curve $y = \frac{e^{1/x}}{x}$ for $x > 0$, together with its minimum point $M$.
(i)[4]

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

(a(i))[4]

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

(a(ii))[3]

Apply the trapezium rule with two intervals to estimate the value of $\int_{1}^{3} \frac{e^{\frac{1}{2}x}}{x}\, dx$, and state your answer correct to 2 decimal places.

(a(iii))[1]

Let the estimate from part (ii) be $E$. Without carrying out any further calculation, explain whether a new estimate obtained from the trapezium rule with four intervals would be greater than $E$ or less than $E$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply the correct quotient rule or product rule

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