Approximate the integral. by using 1+2 (a) Midpoint rule (b) Trapezoidal rule (c) Simpson's rule with...

 

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Approximate the integral. by using 1+2 (a) Midpoint rule (b) Trapezoidal rule (c) Simpson's rule with the stepsizes h=h₂ = 2-k, k=1,2,...16. Using the exact value 1= of given integral, calculate the absolute errors in approximations for each stepsize hy. Plot in one frame the errors against the stepsizes (h) in log-log scale. What do you observe from the plots? Does this confirm the theory for order of convergence? If not, then explain why. 16 Approximate the integral. by using 1+2 (a) Midpoint rule (b) Trapezoidal rule (c) Simpson's rule with the stepsizes h=h₂ = 2-k, k=1,2,...16. Using the exact value 1= of given integral, calculate the absolute errors in approximations for each stepsize hy. Plot in one frame the errors against the stepsizes (h) in log-log scale. What do you observe from the plots? Does this confirm the theory for order of convergence? If not, then explain why. 16

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a Midpoint rule Let n 1h Then the interval 01 is divided into n subintervals of lengt... View the full answer