The formula for polar integration of a circle is ∫02π r2 dθ, where r is the radius of the circle.
Polar integration of a circle involves integrating along the angle θ instead of the x or y-axis. This means that the limits of integration are 0 and 2π instead of a range of x or y values.
Polar integration of a circle is used to find the area enclosed by a circle with a given radius. It can also be used to find the volume of a solid of revolution when the cross section is a circle.
In polar coordinates, the radius of a circle is represented by the variable r. This is different from Cartesian coordinates where the radius is represented by x or y.
One limitation of polar integration of a circle is that it can only be used for circles with a center at the origin. It also cannot be used for circles with a non-constant radius or for circles that do not have a closed form equation.