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

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ENED 1091: Homework #5Due Week of March 30thProblem 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.-0.500.511.522.533.54020406080100X: 3.6Y: 100.6xYX: 3Y: 27X: 2.4Y: 8.175X: 1.8Y: 2.881X: 1.2Y: 1.245X: 0.6Y: 0.736X: 0Y: 1Data Points from Graph:X00.61.21.82.433.6Y10.7361.2452.8818.17527100.6Integral 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))* .6Problem 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.
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 = xx. 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). Calculate the corresponding y-values for the function y = x^x.
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