probability theory – Finding a constant without integration of joint pdf


I have a joint pdf:

$csqrt{1 – x^2 – y^2}, x^2 + y^2 le 1$

I need to find c and I know this can be done by doing the double integration over the possible of values of y and x and equating the result to 1. However, that seems a tedious approach involving trigonometric substitutions. Hence, I’m looking for other suggestions/ approaches to find the constant. Any suggestions?