This question relates to numerical integration a) Sketch the curve y = cos (2x) between x...

  

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This question relates to numerical integration a) Sketch the curve y = cos (2x) between x = 0 and x = 2r. On your sketch clearly mark the area indicated by the following expression and evaluate the expression analytically. 1 = f*cos( cos (2x)dx Explain the difference between analytical and numerical integration and briefly discuss the advantages and disadvantages of both from an engineering perspective. [5 marks] b) Using the Trapezoidal rule determine the area under the curve y = cos (2x) between x = 0 and x = x dividing the area into just three trapezoids each of width(h)= Include a sketch to explain your working. [15 marks] c) Compare the results obtained in part a and part b of this question and explain any difference and how you would increase the accuracy of the numerical solution. [5 marks] This question relates to numerical integration a) Sketch the curve y = cos (2x) between x = 0 and x = 2r. On your sketch clearly mark the area indicated by the following expression and evaluate the expression analytically. 1 = f*cos( cos (2x)dx Explain the difference between analytical and numerical integration and briefly discuss the advantages and disadvantages of both from an engineering perspective. [5 marks] b) Using the Trapezoidal rule determine the area under the curve y = cos (2x) between x = 0 and x = x dividing the area into just three trapezoids each of width(h)= Include a sketch to explain your working. [15 marks] c) Compare the results obtained in part a and part b of this question and explain any difference and how you would increase the accuracy of the numerical solution. [5 marks]