The cross-section of a custom industrial bronze plaque is represented by the region SSS bounded by the lines x=2x = 2x=2, x=12x = 12x=12, the xxx-axis, and the curve
y=8ln(x+5) y = 8 \ln(x + 5) y=8ln(x+5)where all coordinates are measured in centimetres.
Use a single trapezium to calculate an approximation for the area of the cross-section SSS, giving your answer in cm2\text{cm}^2cm2 to two decimal places.
The plaque is manufactured by joining three identical bronze pieces, each with a cross-section equal to region SSS. The bronze sheet has a uniform thickness of 5 mm5 \text{ mm}5 mm and a density of 8.9 g/cm38.9 \text{ g/cm}^38.9 g/cm3.
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 the mass calculated in part (b) could be: (i) an underestimate, (ii) an overestimate.
