Moving into polar coordinates find volume of solid bounded by given surfaces.
$z=x+y,(x^2+y^2)^2=2xy,z=0,(x>0,y>0)$
Moving into polar coordinates we get. $z=r(cos\phi+sin\phi),r^2=sin(2\phi),z=0$
$r(cos\phi+sin\phi)=0$ $\to$ $r=0$ or $\phi=\frac{3\pi}{4}$
But I am having trouble how to set up bounds for $r$ and $\phi.$ 
Set up the volume integration as follows $$ \int_0^{\pi/2} \int_0^{\sqrt{\sin 2\phi}}z \ rdr d\phi= \int_0^{\pi/2} \int_0^{\sqrt{\sin 2\phi}}(\sin \phi+\cos \phi) r^2dr d\phi= \frac\pi8 $$