The region bounded by $x^2 - y = 0$ and $x+y=0$ is rotated around $y=0$
I've drawn a graph of each of these but I'm just not getting it conceptually. The biggest problem I have is knowing when to use the washer/disk/shell method.
2026-04-04 12:09:17.1775304557
How can I find the volume of a solid bounded by these functions?
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Using the washer method,
$$V=\int_{0}^{1} \pi \left( \sqrt{y}^2 - (-y)^2 \right) dy \\ = \int_{0}^{1} \pi (y-y^2)dy$$
Imagine a paraboloid cup-like solid with vertex at the origin, pointing along the y-axis. Then imagine the inside of that cup being shaped like a cone. That's what this solid would look like. You would then use the washer method because the slices perpendicular to the x-axis are shaped like washers.