Symbolic integral simplified doesn't give an error and not simplified does

Hi there.

I had to compute a surface integral for my class, but it started to give an error, so I handed it over to my teacher and she finally found the key point.

syms r theta
dS = sqrt(9/(9-r^2));
mass = int(int(r^2*dS,r,0,3),theta,0,2*pi);

It can't solve the integral and if I try to obtain a numerical value

double(mass)

It just goes crazy and gives me the following error:

Error using symengine
Unable to convert expression into double array.
Error in sym/double (line 672)
        Xstr = mupadmex('symobj::double', S.s, 0);

But if I simplify the expression beforehand (which I just didn't realize to do) as,

syms r theta
dS = 3/sqrt(9-r^2)
mass = int(int(r^2*dS,r,0,3),theta,0,2*pi);

It returns a symbolic value which I can convert to a double,

double(mass)

With no error whatsoever.

This error was the reason why I thought the question of my problem was wrong, so I used r^3 as a factor before dS (which is equal to the square of the distance to the OZ axis by the Jacobian r), and this time it gave no error, although the dS was the same and wasn't simplified either.

syms r theta
dS = sqrt(9/(9-r^2));
mass = int(int(r^3*dS,r,0,3),theta,0,2*pi)
double(mass)

Has anybody have any explanation for this?

I'd really appreacite it, just in case something similar happened to me in some other occasion.

Thanks!

[madhan ravi]

 sqrt(9/(9-r^2))~= sqrt(3/(9-r^2))

[Ricardo J.]

If with ~= you mean equivalent, it's not correct.

sqrt(9/(9-r^2)) ~= 3/sqrt(9-r^2)

[madhan ravi]

Oops, yes your right!

Answer 1

[Walter Roberson]

If you add the int() option 'ignoreanalyticconstraints', true then it can solve the problem.

[Ricardo J.]

How could I do that in my example?

Where should I add that option?

int(int(r^2*dS,r,0,3),theta,0,2*pi)

EDIT:

I found it in the official documentation.

int(int(r^2*dS,r,0,3, 'IgnoreAnalyticConstraints', true),theta,0,2*pi)

And it works.

So thanks!