Doubt in area of an infinitesimally thin ring I want to find out area of a ring of an infinitesimal width in a derivation of electrostatics. So here's how my teacher explained it. Let the inner radius of thin ring be $r$ and outer be $r + dr$.
Area of thin ring
$$dA = π(r + dr)² - πr²
        = π(r² + (dr)² + 2r dr) - πr²
        = π(dr)² +π(2r dr)
        = π(2r dr).$$
My doubt is that why do we ignore the term with $(dr)²$. What determines to ignore a term or contain the term in the expression like $π(2r dr)$ is contained? If we say that $(dr)²$ is infinitesimally small then can't we say that the term with $dr$ is also infinitesimally small to be ignored. 

Consider a dx which is small but finite.  If dx = 1E-6 m, then (dx)^2 = 1E-12 m.  Then add them.
