Warning: Explicit integral could not be found.

Question

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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);

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Answer 1

Roger Stafford 2013-6-26

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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 2013-6-26

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

Walter Roberson 2013-6-26

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

Roger Stafford 2013-6-26

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