Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The sketch illustrates the curve $y = \frac{3}{\sqrt{9 - x^3}}$ for $x$ values between $-1.2$ and $1.2$.
(i)[3]

Use the trapezium rule, with two intervals, to estimate the value of $\int_{-1.2}^{1.2} \frac{3}{\sqrt{9 - x^3}} \, dx$, and give your answer correct to $2$ decimal places.

(ii)[1]

Explain, with reference to the diagram, why the trapezium rule might be expected to produce a close approximation to the actual value of the integral in this case.

Worked solution & mark scheme

This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: The ordinates $0.915929\ldots$ and $1.1112485\ldots$ are stated or implied.

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