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Matlab intergrals

  1. May 6, 2010 #1
    1. The problem statement, all variables and given/known data
    Let us consider an approximation to an integral. Let f(x) be some continuous function on
    [a, b]. We wish to find an approximation for the integral
    I = int from a to b of f(x)dx
    in the following manner:
    Subdivide the interval into N intervals of length h = (b−a)/N. Let xi = ih for i = 0, . . . ,N.
    Let
    Ij = int from 0 to h of f(xj+t)dt

    Find a cubic polynomial Pj (x) that goes through (xj , f(xj)), (xj + h/3,f(xj + h/3)),(xj+2h/3, f(xj+2h/3) and (xj+1,f(xj+1))
    We form an approximation for the integral by letting
    I=sum(j=0 to N-1) of w0*f(xj)+w1*f(xj+h/3)+w2*f(xj+2h/3)+w3*f(xj+1)
    Find these weights, wi.
    In 2 peices of code, plot the first three Bessel functions, J0(x), J1(x) and J2(x), on the
    interval [0, 20]. The first peice of code should be a MATLAB function BJ(x, n) outputing
    the approximation for the integral representation of Jn, given by
    Jn(x) =(1/pi)int from 0 to pi of cos(nt − x sin t)dt
    using the above method for 100 subdivisions of [0, pi]. The second peice of code should call
    the function an produce the required plots with 2000 subdivisions of [0, 20].

    Im just gobsmacked with this qn.. as i only started using matlab a couple of days, ago and have no programming experience.

    what i have done so far is really no good, but i have no idea.

    function [Jn]=BJ(x,n)
    N=100;
    b=pi;
    a=0
    h=(b-a)/N;
    x=a:h:b;
    xj=i*h;
    Ij=0;
    J0=cos(n*xj-x*sin(xj));
    J1=cos(n*(xj+h/3)-x*sin(xj+h/3));
    J2=cos(n*(xj+(2*h/3))-x*sin(xj+(2*h/3)));
    J3=cos(n*(xj+1)-x*sin(xj+1));
    for i=0:N;
    Ij=Ij+w0*J0+w1*J1+w2*J2+w3*J3;
    J=(1/pi)*Ij;
    end

    can someone please help me
     
  2. jcsd
  3. May 7, 2010 #2
    anyone?
     
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