So I was given this question $$x^2 + y^2 + z^2 ≤ 4$$ where $x≥0$, $y≤0$ and $z≤0$. I was told to sketch the $3D$ plot of the region $A$ and the projection region $R$ of $A$ in the $xy$-plane. How do I sketch this? I know its a sphere but how do I sketch it.
2026-03-26 06:27:38.1774506458
The region of integration
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Yes you are on the right track.
The region $A$ isn't a complete sphere rather it is a octant of a sphere.
The region $R$ is a quarter circle.