The cross-section of a custom industrial bronze plaque is represented by the region $S$ bounded by the lines $x = 2$ , $x = 12$ , the $x$ -axis, and the curve

\ln(x + 5)

where all coordinates are measured in centimetres.

Use a single trapezium to calculate an approximation for the area of the cross-section $S$ , giving your answer in $cm2\text{cm}^2$ to two decimal places.

The plaque is manufactured by joining three identical bronze pieces, each with a cross-section equal to region $S$ . The bronze sheet has a uniform thickness of $\text{ mm}$ and a density of $\text{ g/cm}^3$ .

Use the trapezium rule with six ordinates to find an approximate value for the mass of the complete plaque. Give your answer to the nearest gram.

Without further calculation, explain why: (i) the trapezium-rule mass estimate is an underestimate of the mass based on the exact area under the curve, (ii) rounding the ordinates could make the unrounded trapezium-rule mass estimate an overestimate of the estimate found using exact ordinates.

The cross-section of a custom industrial bronze plaque is represented by the region $S$ bounded by the lines $x = 2$ , $x = 12$ , the $x$ -axis, and the curve

\ln(x + 5)

where all coordinates are measured in centimetres.

Use a single trapezium to calculate an approximation for the area of the cross-section $S$ , giving your answer in $cm2\text{cm}^2$ to two decimal places.

Use the trapezium rule with six ordinates to find an approximate value for the mass of the complete plaque. Give your answer to the nearest gram.

3.7.3 Numerical methods (A-level only)

Question 26

Markscheme

3.7.3 Numerical methods (A-level only)

Question 26

Markscheme

3.7.3 Numerical methods (A-level only)

Question 26

3.7.3 Numerical methods (A-level only) Questions

3.7.3 Numerical methods (A-level only)

Question 26

3.7.3 Numerical methods (A-level only) Questions