Compare the integrals of an approximating function and the standard one
This script requires ExT6_2point3 to be run prior
Contents
Define a vector of x-values and evaluate the polynomial s at these values
x = [min(x_given):.001:max(x_given)]; y = eval(s);
Compute the integral of the polynomial numerically
Integral_Approx = trapz(x,y)
Integral_Approx = 1.1127
Compute the integral of the trig function numerically
For T6
Integral_Exact = trapz(x,sin( (pi*x.^2)/2 )) % For T7 %Integral_Exact = trapz(x,exp(x.^2))
Integral_Exact = 1.1048
Compute the difference between the two integrals
Defect = abs(Integral_Approx - Integral_Exact)
Defect = 0.0079
Plot the two curves and the area under the curve
Plot the poly in green
figure; hold on; title('Approximating Trig Integrals via Polynomials') plot(x,y,'og','MarkerSize',10) pause % Plot the sine curve in black plot(x,sin( (pi*x.^2)/2 ),'.k','MarkerSize',10) % For T7 %plot(x,exp(x.^2));
![](CompareIntegrals_01.png)
Create a legend
legend('Polynomial Approximation', 'Exact Function')
![](CompareIntegrals_02.png)