Deriving the Equation for Area of a Ring

[Calpalned]

How was the equation for area of a ring derived?

 

[Calpalned]

I can derive the area as the difference of the areas of two circles. $= \pi(R+dR)^2 - \pi R^2$
But I don't think this $\pi (R+dR)^2 - \pi R^2$ is equal to $(2/pi R)(dR)$ given in the beginning.

 

[PeroK]

I can derive the area as the difference of the areas of two circles. $= \pi(R+dR)^2 - \pi R^2$
But I don't think this $\pi (R+dR)^2 - \pi R^2$ is equal to $(2/pi R)(dR)$ given in the beginning.

No, but it's an approximation for small $dR$.

 

[mathman]

When setting up integrals, the differential is assumed to be vanishing small, so that terms proportional to the powers of the differential can be neglected.