Yes, it's all good. (Yes)PullandTwist said:
A double integral in polar coordinates is a type of integration that is used to find the volume or area under a curve in the polar coordinate system. It involves integrating over a region in the form of a circular sector or a polar rectangle.
In a double integral in polar coordinates, the region of integration is defined using polar coordinates (r and θ) instead of rectangular coordinates (x and y). This allows for a simpler representation of curves and regions that are more naturally defined in polar coordinates.
The formula for calculating a double integral in polar coordinates is ∫∫f(r,θ) rdrdθ, where f(r,θ) is the function being integrated and the limits of integration are determined by the region of integration.
Double integrals in polar coordinates are commonly used in physics and engineering to calculate moments of inertia, center of mass, and gravitational potential. They are also used in calculating areas and volumes in curved regions, such as circles, ellipses, and other polar curves.
Some common mistakes to avoid when working with double integrals in polar coordinates include forgetting to convert the limits of integration from rectangular to polar coordinates, forgetting to include the extra r term when integrating, and using the incorrect formula for the region of integration (i.e. using a polar rectangle formula for a circular sector).
