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HW5 - ENED 1091 Homework#5 Due Week of March 30th Problem 1...

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ENED 1091: Homework #5 Due Week of March 30 th Problem 1 : Use the data points show below and the trapezoidal rule to estimate the integral of the curve shown below from t = 0 to 3.6. Be sure to clearly show your calculations – don’t just give an answer. -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 0 20 40 60 80 100 X: 3.6 Y: 100.6 x Y X: 3 Y: 27 X: 2.4 Y: 8.175 X: 1.8 Y: 2.881 X: 1.2 Y: 1.245 X: 0.6 Y: 0.736 X: 0 Y: 1 Data Points from Graph: X 0 0.6 1.2 1.8 2.4 3 3.6 Y 1 0.73 6 1.24 5 2.88 1 8.17 5 27 100.6 Integral Estimate (Trapezoid): ________50.9022____________ Calculations: x = [0 .6 1.2 1.8 2.4 3 3.6]; y = [1 .736 1.245 2.881 2.175 27 100.6]; g = (1/2 * y(1)+ y(2) + y(3)+ y(4) + y(5)+ y(6) + 1/2* y(7))* .6 Problem 2 : Repeat Problem 1 using Simpson’s Rule to estimate the integral of the curve from x = 0 to 3.6. Be sure to clearly show your calculations – don’t just give an answer.
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Integral Estimate (Simpson’s): _________46.1816___________ Calculations: x = [0 .6 1.2 1.8 2.4 3 3.6]; y = [1 .736 1.245 2.881 2.175 27 100.6]; g = .6/3 * (y(1) + 4*y(2) + 2*y(3) + 4*y(4) +2*y(5) + 4*y(6) + y(7)) Problem 3: The curve shown in problem 1 is for the function y = x x . There is no expression for the indefinite integral of this function. However, we can estimate the definite integral using numerical integration as you have done in Problems 1 and 2. Write a MATLAB script that will: Begin with 3 data points (x-values) evenly distributed from 0 to 3.6 inclusive (Hint: linspace).
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