Simpson's rule

Given that

complete the table below with the value of y corresponding to x = 2, giving your answer to 2 decimal places.

Use Simpson’s rule, with all the values of y in the completed table, to estimate, to one decimal place, the value of

Using your answer to part (b) and making your method clear, estimate the value of

Given that

complete the table with the value of y corresponding to x = 3, giving your answer to 4 significant figures.

In part (b) you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

Use Simpson’s rule with all the values of y in the completed table to estimate, to 3 significant figures, the value of

Using your answer to part (b) and making your method clear, estimate the value of

Use Simpson’s rule with 4 intervals to find an estimate for

Give your answer to 3 significant figures.

Given that ₀²e^sin2x dx = 3.855 to 4 significant figures,

comment on the accuracy of your answer to part (a).

Figure 1 shows a sketch of the vertical cross-section of the entrance to a tunnel. The width at the base of the tunnel entrance is 2 metres and its maximum height is 3 metres.

The shape of the cross-section can be modelled by the curve with equation y= f (x) where

A wooden door of uniform thickness 85 mm is to be made to seal the tunnel entrance.

Use Simpson’s rule with 6 intervals to estimate the volume of wood required for this door, giving your answer in m³ to 4 significant figures.

Use Simpson’s rule with 4 intervals to estimate