Homework 3

Homework 3 - 8 A >%This program uses the Composite...

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8. A) >> %This program uses the Composite Trapezoidal Rule to approximate the integral% >> x = sym('x'); >> f = x^2*exp(-x^2); >> a=0; b=2; n=8; >> h = (b-a)/n; >> trapsum = vpa(subs(f,x,a)) + vpa(subs(f,x,b)); >> for i=1:n-1, trapsum = trapsum + 2*vpa(subs(f,x,a+i*h)); end >> trapsum = .5*h*trapsum trapsum = .42158203719810195819750475720865 8. B) >> %This is a program that calculates the approximation of an integral using Simpson's% >> a=0; b=2; n=8; >> a=0; b=2; n=8; >> h = (b-a)/n; >> x = sym('x'); >> f = x^2*exp(-x^2); >> simpsum = vpa(subs(f,x,a)) + 4*vpa(subs(f,x,a+h))+vpa(subs(f,x,b)); >> for i = 1:(n-2)/2, simpsum = simpsum+4*vpa(subs(f,x,a+(2*i+1)*h)); simpsum = simpsum+2*vpa(subs(f,x,a+2*i*h)); end >> simpsum = h * simpsum/3 simpsum = .42271618793397650049037395092453

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8. C) >> %This is a program that calculates the approximation of an integral using the Midpoint Rule% >> a=0; b=2; n=8; >> h = (b-a)/n; >> x = sym('x'); >> f = x^2*exp(-x^2); >> midsum = vpa(subs(f,x,a)) + vpa(subs(f,x,b));
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Homework 3 - 8 A >%This program uses the Composite...

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