Im having trouble figuring this integral out can someone help? Not allowed to use polar coordinates. $$c\int_{-1}^{1} \int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\sqrt{1-x^2-y^2}dy \:dx=1 .$$ Find $c.$ I went with the substitution say $b=1-x^2$ in the first integral. Then I went with : $\cos t= {y \over \sqrt{b}}$ Could anyone finish the integral with this, i'm very inteerested as to find out how to solve this?

In the inner integral over $y$, use the substitution
$$y=\sqrt{1-x^2}\cdot \sin\theta$$
for $-\frac{\pi}2\le \theta\le\frac{\pi}2$.
Then in (part of) your remaining integral over $x$, use the substitution
$$x=\sin\phi$$
for $-\frac{\pi}2\le \phi\le\frac{\pi}2$.
You should be able to finish from here.
