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matlabcalculusintegral

integration example with matlab

Can someonse show me how to calculate the following in matlab:

enter image description here

where

g = 9.91
As = 1000
z = 10
zv = 30
zD = 10
pz = 999
Az = 500
Solution

  • Well, there are a couple of ways to go about this:

    Analytical approach

    Like Rudy commented, this is a trivial integral to do analytically because it's the integral of a power (z1). Its indefinite integral would be:

    F(z) = (g/As)(z2/2 - zvz)pzAz

    According to the Second Fundamental Theorem of Calculus, the definite integral is computed by substituting the integral bounds into F(z), that is:

    ST = F(zd) - F(0) = (g/As)(zD2/2 - zvzD)pzAz

    In MATLAB, that would be:

    ST = g / As * zD * (zD / 2 - zv) * pz * Az
ST = 
      -1.2375e+06

    Numerical approach

    If, for some reason, you want to calculate that numerically by approximating the integral, you can use the trapz function for this:

    dz = 0.001; z = 0:dz:zD;
y = g / As * (z - zv) * pz * Az;
ST = trapz(z, y)
ST = 
      -1.2375e+06

    or make an even cruder approximation with a simple sum:

    ST = sum(y * dz)
ST =
      -1.2387e+06