When trying to find the electric field created by a uniformly charged disc at a point P on axis of the disc, it can be done by integration.

[![enter image description here][1]][1]

We start by finding the electric field dE created by each infinitesimal disc of thickness da, as shown in the picture.

The area of each infinitesimal ring is said to be 2*pi*a*da. 

Shouldn't it be pi*(a+da)^2 -pi*a^2? Because it should be the area of the large ring of radius (a+da) minus the smaller ring inside of radius a to find the area of just the ring thickness da?

I suspect it's something to do with the expansion of what I believe it should be, because I'm not exactly sure what (da)^2 would equal? Is this the error?

  [1]: https://i.sstatic.net/94HhK.png