Multiple integral with a parameter

[gipc]

Let D be the following circle with the radius a.
http://img580.imageshack.us/img580/6402/97833345.jpg

Find the parameter a for which f(a) gets its minimal value.
http://img844.imageshack.us/img844/2993/91289562.png

 

[hunt_mat]

Change the integral to polars and do the integral. You will get a function of a as the answer, differentiate w.r.t. a to find the minimal value.

Mat