The cone of an aircraft can be modelled be rotating an ellipse about the x-axis as...

 

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The cone of an aircraft can be modelled be rotating an ellipse about the x-axis as shown below: To estimate the amount of material required to construct the cone it is necessary to find the surface area, which is given by the integral π/2 :! cos(9)√4-3 sin² (9) do S = 4 T Working to 6 decimal places, complete the following table of values for f(9) = cos(9)√4-3 sin² (9) 0 TL 16 IT 8 3 π 16 2π + π 4 f(9) Hence estimate the area using i) Trapezium Rule ii) The exact answer for the area, S, is given by 5 п 16 8 8 π² √√√3 9 3 πT Simpsons Rule. 7 п 16 T 2 Calculate the error for both methods and comment on your answers. [10 marks] The cone of an aircraft can be modelled be rotating an ellipse about the x-axis as shown below: To estimate the amount of material required to construct the cone it is necessary to find the surface area, which is given by the integral π/2 :! cos(9)√4-3 sin² (9) do S = 4 T Working to 6 decimal places, complete the following table of values for f(9) = cos(9)√4-3 sin² (9) 0 TL 16 IT 8 3 π 16 2π + π 4 f(9) Hence estimate the area using i) Trapezium Rule ii) The exact answer for the area, S, is given by 5 п 16 8 8 π² √√√3 9 3 πT Simpsons Rule. 7 п 16 T 2 Calculate the error for both methods and comment on your answers. [10 marks]