Int() returning incorrect answer

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I need to solve a double integral, using symbolic variables. My code is as follows:
stiff = transpose(B)*E*B*t*detJ;
K = int(int(stiff,zeta,-1,1),eta,-1,1)
where zeta and eta have been defined as symbolic variables and stiff is an 8x8 matrix.
I have been given the precise answers, so I know that everything leading up to the K calculation is correct. However, K doesn't match at all. Does anyone have insight on why the integral isn't correct?
  2 Comments
Jennifer Hansen
Jennifer Hansen on 26 Nov 2022
Ah, it does, I just didn't include the rest because I know it's correct. Thank you for your response! I actually did something very silly and used a constant E instead of my E matrix, which I named something else. I was concerned I was misunderstanding how to use int().

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Accepted Answer

Walter Roberson
Walter Roberson on 26 Nov 2022
Especially in the case of trig expressions or expressions that integrate to trig (such as ones that integrate to arctan), then int() is permitted to return any mathematically equivalent expression. You should subtract the returned expression from the known answer and evaluate at several points to determine whether the expressions are equivalent.
For example if you integrate sin() you will not necessarily get back an expression in cos: you might get back something based on the fact that sin-squared plus cos-squared equals 1.
  1 Comment
Steven Lord
Steven Lord on 27 Nov 2022
Instead of evaluating at several points to do a probabilistic equivalence test, I recommend using the isAlways function.
syms x
f1 = sin(2*x)
f1 = 
f2 = 2*sin(x)*cos(x)
f2 = 
isAlways(f1 == f2)
ans = logical
1
f3 = cos(x).^2-sin(x).^2 % cos(2*x)
f3 = 
f4 = cos(2*x)
f4 = 
isAlways(f1 == f3)
Warning: Unable to prove 'sin(2*x) == cos(x)^2 - sin(x)^2'.
ans = logical
0
isAlways(f3 == f4)
ans = logical
1

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