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.

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 2pia*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?