Past exam of the mathematical methods II course of the University of Oxford / 2016 resit / 2 / ii

For $-1\le y\le 0$, a horizontal slice runs from $x=-1$ to the line $x=y$. For $0\le y\le 1$, it runs from $x=-1$ to the negative branch $x=-\sqrt{y}$ of the parabola. Thus the reversed iterated integral isThe positive branch $x=\sqrt{y}$ is outside the original integration region.