Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram illustrates 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]

Use the trapezium rule with two intervals to estimate the area of region $A$. Give your answer correct to 2 decimal places.

(ii)[2]

Deduce an approximation to the area of region $B$ and explain why this approximation underestimates the actual 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 imply correct ordinates $(1, \sqrt{2})$ or $(1, 1.414)$ and $(3, 3)$

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