I was given this question to answer:
x2+ y2 = 4 rotates about y = 2
I know how to find volume when I have 2 functions and their the outer and inner radius (distances from the rotation axis). What is the approach to this question? Thank you!
2026-04-12 07:41:44.1775979704
Integral that represents the volume of the solid obtained by rotating an ellipse about a line.
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The approach is very similar. For example, if we use shell method,
Shell width at $y$ (distance from x-axis) is $2 \sqrt{4-y^2}$.
Radial distance of the shell from $y = 2$ is $(2 - y)$ where $ - 2 \leq y \leq 2$.
Now, can you you complete the working?