Prove this integral, the Dirichlet's formula

Question

Show that $$\int\int_R x^{p-1}y^{q-1}dxdy = \frac{\Gamma(\frac{p}{2})\Gamma(\frac{q}{2})}{\Gamma(\frac{p}{2}+\frac{q}{2}+1)},$$ where R is the region bounded by the first quadrant of the circle $$x^2 +y^2=1$$

Answer 1

Hint: Aim for the Beta function and use the identity $$B(a, b)=\frac{\Gamma(a)\Gamma(b)}{\Gamma (a+b)}.$$

Answer 2

Here is how you advance

$$\int_{0}^{1} \int_{0}^{\sqrt{1-y^2}} x^{p-1} y^{q-1} dx dy.$$

Check $\beta$ function to finish the problem.