# How to explain a difference in solutions of integrals between MATLAB and MAPLE?

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Dear community,

after solving an integral via MAPLE 2022 (see the solution in blue),

I tried to reproduce the calculation in MATLAB R2021b as a numerical and symbolic expression:

%% integral: numerical expression

%empirical coefficents

vrel = 0.000018;

alpha = 0.08;

beta = -6.75;

h =1;

d =1;

%function

fun = @(theta) (alpha*beta*cos(theta).^4).*(pi*d-8*beta*vrel*cos(theta).^2).^(-2);

%integral

F = integral(fun,0,pi/2)

%% integral: symbolic expression

%system parameters

syms theta alpha beta d vrel

%function

fun = (alpha*beta*cos(theta).^4).*(pi*d-8*beta*vrel*cos(theta).^2).^(-2);

%substiution of empirical coefficents

fsub = subs(fun,{alpha, beta, d, vrel}, {0.0814,-6.75,1,0.000018});

%integral

f = int(fsub,theta,0,pi/2);

%evaluation for complex number

c = subs(f, 1+i);

F = double(c)

However, the solution between MATLAB and MAPLE differs by 8 magnitudes. My colleauge and me double-checked for typos but couldn't figure out any. I verified the result from MAPLE via comparison to a simplfied solution for the integral.

I am curious to learn about my mistake(s) when adapting the integral into MATLAB!

##### 3 Comments

Bjorn Gustavsson
on 10 Nov 2022

### Accepted Answer

Jiri Hajek
on 10 Nov 2022

Nicely done graphs! So, just by looking at the graphs, it is clear that:

- The integral of your function is a negative value, with lower limit on the value being the area of the graph, i.e. about 1,6x(-0,05)= - 0,08
- Comparing your original results from MATLAB with the above, it seems that both provide good estimates, although it remains to see which one is more precise
- The MAPLE result is a complete nonsense, 8 orders of magnitude off the target.You have to search for error in your MAPLE implementation, not in MATLAB.

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