# MAE305_P4.docx - Jaber 1 California State University Long...

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Jaber 1 California State University Long Beach Mechanical and Aerospace Engineering Department MAE 305 Project #4: Solving Integrand Utilizing Numerical Methods Submitted by: Hussein Jaber Section #3 Due Date: 4/28/2020
Jaber 2 Introduction: In this project, we will be using solving the following Integrand numerically: The integral will be solved initially by a basic hand calculation. After the integral has been solved by hand calculation, it will again be solved using numerical methods in MATLAB. The methods that will be used here will be the Rectangular Rule, Trapezoidal Rule, 3/8 Simpson’s Rule, and finally using Gaussian Quadrature. The rectangular rule will be using left-endpoints, with 10, 100, and 1000 intervals. The trapezoidal and 3/8 Simpson’s rules will both utilize 10, 100, and 1000 intervals as well. Lastly, Gaussian Quadrature will be with nodes 2, 4, and 6.
Jaber 3 A. By hand calculation:
Jaber 4 B. Rectangular Rule: Code:
Jaber 5 Solution: C. Trapezoidal Rule: Code:
Jaber 6 Solution: D. 3/8 Simpson’s Rule: Code:
Jaber 7 Solution: E. Gaussian Quadrature: Code:
Jaber 8 Solution: Results: Method: Value Error Hand Calc. 600 0% Rectangular n=10: 466.4000 n=10: 22.3%
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