Write a function called approximateIntegral that uses a loop

Write a function called approximateIntegral that uses a loop to compute a numerical approximation that adaptively changes ?x to smaller and smaller step sizes, until the approximation is accurate and precise within the number of decimal points defined by precision (difference between approxi+1 and approxi must be less than 1

Solution

function res = approximateIntegral( dx,refinement,precision )

approx = [];
j=1;
error = 10000;

increment = 1/dx;

increment = ceil(increment);
dx = 1/increment;

dx_a(1) = dx;

sum=0;
for i=1:dx:2
    sum = sum + sin(i)*dx/i;
end

approx(j) = sum;
j=j+1;
dx = dx*refinement;

while(error > 10^-precision)
  
    increment = 1/dx;
  
    increment = ceil(increment);
    dx = 1/increment;
    dx_a(j)=dx;
  
    sum=0;
    for i=1:dx:2
        sum = sum + sin(i)*dx/i;
    end
  
    approx(j) = sum;
    error = abs(approx(j)-approx(j-1));
    dx = dx*refinement;
    j=j+1;
  
end

res = [dx_a\' approx\'];

end