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MATLAB Trapezoidal RuleConsider the function y=f(x) for the interval a≤x≤b, shown in figure: 
To evaluate the definite integral, The total area is: 
 plus the area of the trapezoid x1 P1 P2 x2 that is equal to  , and so on. Then, the trapezoidal approximation becomes
ExampleUsing the trapezoidal rule with n=4, estimate the cost of the definite integral 
Compare with the exact value and evaluate the percent error. Solution: The exact value of this integral is 
For the trapezoidal rule approximation, we have 
and by substitution into an equation 
From equation 3 and equation 4, we find that the percent error is 
Next TopicMATLAB Trapz
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dx, we divide the interval a≤x≤b into subintervals each of length
. Then, the number of points between x0=a,and xn=b is x1=a+∆x,x2=a+2∆x,…xn-1=a+(n-1)∆x. Therefore, the integral from a to b is the sum of the integrals from a to x1, from x1 to x2 and so on, and finally from xn-1 to b.
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