A-LevelMathematicsNumerical methods9709/32 · Oct/Nov 2017 · Q14 Marks
The diagram shows a sketch of the curve y = 3 / √(9-x³) for values of x from -1.2 to 1.2. [Figure 1.1]
- (i)Use the trapezium rule, with two intervals, to estimate the value of ∫(-1.2 to 1.2) (3 / √(9-x³)) dx, giving your answer correct to 2 decimal places.[3]
- (ii)Explain, with reference to the diagram, why the trapezium rule may be expected to give a good approximation to the true value of the integral in this case.[1]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [1] State or imply ordinates 0.915929..., 1, 1.112485...
- [1] Use correct formula, or equivalent, with h = 1.2 and three ordinates
- [1] Obtain answer 2.42 only
- [1] Justify the given statement
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