Maurice Tutor

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    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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    Oct-2001 - Nov-2016

Category > Management Posted 03 Apr 2018 My Price 9.00

value of the integral

Write a user-defined MATLAB function for integration with the composite Simpson's method of a function /(x) that is given in a set of n discrete points that are spaced equally. For the function name and arguments use I=SimpsonPoints (x, y), where the input arguments x and y are vectors with the values of x and the corresponding values of f(x), respectively. The output argument I is the value of the integral. If the number of intervals in the data points is divisible by 3, the integration is done with the composite Simpson's 3/8 method. If the number of intervals in the data points is one more than a number divisible by 3, the integration in the first interval is done with the trapezoidal method and the integration over the rest of the intervals is done with the composite Simpson's 3/8 method. If the number of intervals in the data points is two more than a number divisible by 3, then the integration over the first two intervals is done with Simpsons's 1/3 method and the integration over the rest of the intervals is done with the composite Simpson's 3/8 method.

(a) Use SimpsonPoints to solve Problem 9.1 .

(b) Use SimpsonPoints to solve Problem 9.5.

Problem 9.1

The function (x) is given in the following tabulated form. Compute

with h = 0.3 and with h = 0.4

(a) Use the composite rectangle method.

(b) Use the composite trapezoidal method.

(c) Use the composite Simpson's 3/8 method.

 

 

Problem 9.5

The Head Severity Index (HSI) measures the risk of head injury in a car crash. It is calculated by

where a(t) is the normalized acceleration (acceleration in m/s2 divided by 9.81 m/s2 ) and tis time in seconds during a crash. The acceleration of a dummy head measured during a crash test is given in the following table

Determine the HSI. (a) Use the composite trapezoidal method.

(b) Use the composite Simpson's 1/3 method.

(c) Use the composite Simpson's 3/8 method.

 

Answers

Maurice Tutor
(5)
Status NEW Posted 03 Apr 2018 08:04 PM My Price 9.00

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