Hello, I\'ve been having touble trying to find out how to write the MATLAB code

Question

Hello, I've been having touble trying to find out how to write the MATLAB code for the function given as:

Function c = reimsum(P,a,b,n)

which accepts as inputs, a polynomial P and three scalars a, b, and n. Returning a scalar c which gives the Riemann sum approximation of the definite integral. So the function will use Riemann sums to approximate the definite integral of the polynomial on the interval [a,b]. Then it will use n subintervals of equal length with the value of the function taken at the midpoint of each subinterval.

Since the polynomials must be typed through the standard basis, the commandx=sym(‘x’) is needed from my understanding.

The function could use for loop, the commandsym2poly, and the MATLAB function polyval.

Explanation / Answer

function r=reimsum(f,a,b,n)
dx=(b-a)/n;
% initialize r to f(a) (the left-end point of the first sub-interval
% [a,a+dx])
r=f(a);
% need only consider the n-1 remaining sub-intervals
for k=1:n
c=a+k*dx;
r=r+f(c);
end
r=dx*r;
end

F = @(x) 2*x;
>> reimsum(F,0,1,10)

ans =

1.1000

F = @(x) (2.*x.^2+x+1);
>> reimsum(F,0,1,10)

ans =

2.4200

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