Integrating using sums(riemann sums)

Hi, i want to find the integral of function f without using the int function with the limits 5 and 17 . I want to find the riemann sum of the function f.

I tried solving it by using the int function but now i want to find the area withou using int. below is my code but n should represent the number of divisions that gives an accuracy of 10^-4 , i am not sure if my value of n is correct or not? how do i find n and the area (c) ?please help.

format longG
syms x
f = 2*pi*(0.16*(0.25-(x-1)^2)+44.52)*(1+(-0.32*x - 0.32)^2)^1/2;
a = int(f,5,17.688);
b = sym(a);
c = double(b);
n = (17.688-5)/0.0001;
SurfaceArea = [c n]

Answer 1

[Birdman]

You may use rsums. It allows you to interactively calculate the riemann sum integral:

rsums(f,5,17.688)

Riemann Sum Integral

[WILLBES BANDA]

Thank you for your answer

but this works exactly the same as int function, cant we form a loop that calculates the area of each rectangle under the graph and then sum up to give us the overall area without using functions like int or rsums? Please help.

[Birdman]

f=@(x) 2*pi*(0.16*(0.25-(x-1)^2)+44.52)*(1+(-0.32*x - 0.32)^2)^1/2;
dt=0.0001;
N=5:dt:17.688;
riemannSumIntegral=0;
for i=1:numel(N)
    riemannSumIntegral=riemannSumIntegral+f(N(i))*dt;
end

[WILLBES BANDA]

it works perfectly fine, at least i will have to find the number of divisions(n) required for the area to have an accuracy of 10^-4 . Thank you honourable

[Steven Lord]

Is that possible to do? Sure.

If you're asking us to write it and post, I'm hesitant to do so as that feels like a fairly common homework assignment in a numerical analysis course.

If you've written such a function and need help diagnosing and fixing a problem with it, post your function, the problem you're trying to solve, and an explanation of the problem you're experiencing and we may be able to offer some guidance.

[WILLBES BANDA]

From the code that i wrote above as part of the question, the number of divisions is represented by n. And i took the difference between the interval and divided it by 0.0001 but i still get a wrong answer. So i also need help diagnosing and fixing the problem with finding the number of divisions, apologies for not being more clear when posting the question.

[Torsten]

You got an answer from your own code ? Where is this code ?

[WILLBES BANDA]

this was my initial code that was part of the question and i am trying to figure out the number of divisions required to get an accuracy of 10^-4

format longG
syms x
f = 2*pi*(0.16*(0.25-(x-1)^2)+44.52)*(1+(-0.32*x - 0.32)^2)^1/2;
a = int(f,5,17.688);
b = sym(a);
c = double(b);
n = (17.688-5)/0.0001;
SurfaceArea = [c n]

[Torsten]

Take the result from int as the correct value for the integral.

Then test which values you get for the integral for h=1e-2,1e-3,1e-4,... using Riemann sums and compare with the value you got from int. As soon as the difference between the values is smaller than1e-4, you got the adequate step size. Note that it's usually not possible to determine the h in advance,only by testing.

[WILLBES BANDA]

Noted. Thank you Honourable

[Elvin]

I tried this but it says "unrecognized function"