OkayShell Method?
What does the single x there represent in your shells?V= 2pi * ∫x* f(x) dx, where a and b are the lower and upper limits of integration, respectively.
Do you have constant x or constant y within your shells? That is fine.And how do I know to use dx or dy?
Right.and so I would have to add 1
The integration variable ("dx") determines that radius.But I don't even understand what quantity defines the radius here.
The volume of a solid by revolution is the amount of space occupied by the solid when it is rotated around a specific axis. It is a measure of the three-dimensional space inside the solid.
The formula for calculating the volume of a solid by revolution is V = π∫ab (f(x))2dx, where a and b are the limits of integration, f(x) is the function representing the cross-sectional area of the solid, and π is the constant pi.
The axis of revolution is the imaginary line around which the solid is rotated. It can be any line passing through the solid's center of mass or any other point on its surface.
No, the volume of a solid by revolution cannot be negative. It is always a positive value as it represents the amount of space occupied by the solid.
Calculating the volume of a solid by revolution is used in various fields such as engineering, architecture, and physics. It is used to design and analyze structures like bridges, buildings, and tunnels. It is also used in the study of rotational motion and fluid dynamics.