Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram displays the curve $y = \sqrt{1 + x^3}$. Region A is enclosed by the curve together with the lines $x = 0$, $x = 2$ and $y = 0$. Region B is enclosed by the curve together with the lines $x = 0$ and $y = 3$.
(i)[3]

With two intervals, apply the trapezium rule to estimate the area of region A. Give your answer correct to 2 decimal places.

(ii)[2]

Find an approximation to the area of region B and explain why this approximation is an underestimate of the true area of region B.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Show or make clear the correct ordinates $1,\sqrt{2}$ or $1.414,3$

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