Why does MATLAB (Symbolic Math Toolbox) not integrate this simple function.
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I am trying to integrate the following function symbolically, but MATLAB won't resolve this.
syms x a
int((1-x^2/a^2)^(3/2),x,-a,a)
It should be 
and Wolfram Alpha calculates it without problem. Is there a way to get this result in MATLAB too?
and Wolfram Alpha calculates it without problem. Is there a way to get this result in MATLAB too?回答（3 个）
Your problem is, you need to define a properly. So, if you do only this:
syms x a
I = int((1-x^2/a^2)^(3/2),x)
Now you see that MATLAB finds a solution, but it does not know anything about a. We can try this, but MATLAB is still confused.
simplify(subs(I,a) - subs(I,-a))
The problem there is, if a takes on some general complex value, that result may not be a simple thing. The point being:
syms a
simplify(a*sqrt(-1/a^2))
syms a real
simplify(a*sqrt(-1/a^2))
For real a, that last one reduces to +/-i, depending on the sign of a.
syms a real positive
simplify(a*sqrt(-1/a^2))
Only in the third case does a drop out completely.
So if we specify a more clearly.
syms x
syms a real positive
I = int((1-x^2/a^2)^(3/2),x)
simplify(subs(I,a) - subs(I,-a))
syms x a real
I = int(simplify((1-x^2/a^2)^(3/2)),x,-a,a)
2 个评论
This works as I hoped. Thanks. It is still strange that it works with the exponent 1/2
syms x a
int((1-x^2/a^2)^(1/2),x,-a,a)
and with the exponent 2
int((1-x^2/a^2)^(2),x,-a,a)
without the simplify but not with 3/2.
int((1-x^2/a^2)^(3/2),x,-a,a)
Paul
2022-6-3
Sometimes int() works in mysterious ways, I suppose. I believe I've seen other case where int() does not return a solution w/o manipulating the integrand into a different form.
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2022-6-3
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