first integrate for the dr integral, where z is constant. add and subtract z² and split the integral and u can solve for the dr. then r is constant and solve for z. did u try it this way?
Ok, finally, I solved the problem and posting the solution here. It took me 5 minutes to complete it and 1 hour to type it in LATEX! you owe me one!
i have checked the solution with a couple of sample inputs, and turned out to be right. however, in case you find it wrong, i advise you to go thro the solution and check for the mistakes for i hope the method to be right, only some calculation errors shud be there, IF any.
cedance.
PS: v_c, the solution to your integral is right, but you have typed the LHS wrong i guess, its to the power 3/2 not 1/3. u have written the cube root expression??