MaplePrimes - answers and comments on Question, How do I calculate Riemannsum?

Homework?

hirnyk — Sat, 05 Mar 2011 23:13:06 Z

It looks like a homework. What did you do on your own? In order to produce you request, the integral int(1/(1+x^2),x=0..1)=Pi/4 can be taken into consideration. Look at ?Riemannsum . The error of this approximation in the case of equal-sized subintervals is the same as the error of the trapezoidal approximation up to multiplier 2. See sec_5-2.pdf for that. Don't hesitate to ask me and my colleagues in the need. Of course, this is your work which you must do.

PS. Increase the partition option until the difference between the upper Riemann sum and the lower Riemann sum will become less than 0.0001/4.

Trapezoidal approximation dosent work

Harry_smile — Sun, 06 Mar 2011 17:53:36 Z

I'm supposed to get the answer S[41]=3.141493506 but I don't understand what I'm doing wrong

operation

Harry_smile — Sun, 06 Mar 2011 17:58:45 Z

This is the operation I've done

f:=x->4/(1+x^2);

n:=1;s[n]:=1;while abs(s[n]-Pi)>=0.0001 do n:=n+1;s[n]:=evalf(sum(f((k-1)/n+k/n)*1/2n),k=1..n));end do; E[n]:=evalf(abs(s[n]-Pi));

but it doesn't work....

still doesn't work

Harry_smile — Sun, 06 Mar 2011 19:42:13 Z

I have now put in evalf before Pi

f:=x->4/(1+x^2);

n:=1;s[n]:=1;while abs(s[n]-evalf(Pi))>=0.0001 do n:=n+1;s[n]:=evalf(sum(f((k-1)/n+k/n)*1/2n),k=1..n));end do; E[n]:=evalf(abs(s[n]-Pi))

but still no....

Syntax and math

hirnyk — Sun, 06 Mar 2011 19:14:56 Z

At least, there are two mistakes in your code.

1. Look at ?do . The construction for n from ... to .. must be before while .

2. The right trapezoid formula is s := sum(evalf((f((k-1)/n)+f(k/n))/(2*n)), k = 1 .. n) .

PS. The most serious defect of your code is that you don't know Pi, you calculate it. Because of this you have to use another stop condition.