I am not really sure if I am on the right track right now. But I am supposed to find the volume of the solid.
My Attempt (Volumes of Revolution):
So I am given the following equations: $$\begin{align*} y = 1-x^2 \quad (1)\\ y = 0 \quad (2)\\ x = 0 \quad (3) \end{align*}$$
So first, I tried to find the points of intersection of these equations. For (1) and (2), I let them equal to each other and found that they intersect at $x = \pm 1$. And for (1) and (3), I sub (3) to (1) and I found that they intersect at $y = 1$.
I am not exactly sure where to proceed from here. Any help would be great!
Firstly we must translate all points and curves $2$ units down, so we will end up rotating about the $x$ axis, which is manageable. So, the area we are concerned with is now bounded by the curves $$\begin{align} & x=0\\ & y=-2\\ & y=-1-x^2 \end{align}$$ Let's find the intersection points of the curves. Let $y=-2$. Then $x^2=1$ so $x=1$ (assuming you just mean the area bounded in the last quadrant, as there are $2$ possible quadrants you could be talking about, as noted in comments).
Hence the volume generated will be equal to
$$\pi\int_0^1 (-2)^2-(-1-x^2)^2dx$$ Can you finish? Please tell me if you need more help and I will be happy to comply.