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Question: computing a principal value integral

Question:computing a principal value integral

bprotas 52 Maple
February 23 2010
0

Dear All,

I wonder if anyone could perhaps offer some advice concerning evaluation of the following definite integral in closed form.  The integral is defined in the principal value sense and arises in a problem involving integration over an ellipse with the axes given by a and b. The command int(...) (see below) used in Maple 13 does not seem to deliver any result in finite time. Thanks a lot!  Bartek
 


>assume(p,real); assume(q,real);
>assume(a,real); assume(b,real); additionally(a>b);
>integrand := cos(q)*(b^2*cos(q)^2+a^2*sin(q)^2)/(a*cos(p)+I*b*sin(p)-a*cos(q)-I*b*sin(q));
>int(integrand,q=0..2*Pi,'CauchyPrincipalValue');
Warning,  computation interrupted

 
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