Warning: Explicit integral could not be found.

Hi

I'm trying to solve this integral but it gives me this error: Warning: Explicit integral could not be found.

 syms a b
 Q = (1/(2*pi*lams)) * exp( - (a^2 + b^2)/(2*lams));
 q = int(int(Q,b,0,sqrt((lams^2) - (a^2))),a,0,lams);

Answer 1

[Roger Stafford]

Apparently 'int' is not quite smart enough to make a change of variables. If you change the variables to polar coordinates:

 a = r*cos(theta)
 b = r*sin(theta)

the double integral is easily found and has the value (if my calculus isn't too rusty)

 q = 1/4*(1-exp(-lams/2))

(The area covered by the integration in the a,b coordinates is a quarter circle.)

Answer 2

[Walter Roberson]

It does not have any obvious closed form integral. Do you have reason to expect that there is a closed form for it?

[Roger Stafford]

But it does, Walter, as I have just pointed out, but 'int' is not able to find it.

[Walter Roberson]

My answer was being prepared before yours was posted ;-)

[Roger Stafford]

I'm sorry. I should have made allowance for that before complaining.