The formula for calculating the volume of revolution is V = π∫(R(x))^2 dx, where R(x) is the radius of the cross-sectional area at a given x-value.
The limits of integration for VOR are determined by setting the given equation equal to the variable of integration (in this case, x) and solving for the corresponding y-values. These y-values will be the upper and lower limits of integration.
VOR can be used for any shape that can be formed by rotating a function around the x-axis. This includes circles, squares, rectangles, and more complex shapes.
VOR is typically used for definite integrals, as it requires specific limits of integration. However, it is possible to use it for indefinite integrals by setting the lower limit of integration to a constant and the upper limit to x. This will result in a general equation for the volume of revolution.
VOR has limitations when the shape being rotated intersects with the axis of revolution. In these cases, a different method, such as the disk or washer method, should be used. VOR also assumes that the shape being rotated is continuous and has a defined upper and lower bound.