# What do we call this small area in integration in math?

In the above image we can see to find area of circle they consider the very small annulus with area of $$\delta A=2\pi r \delta r$$. and in order to to find $$\int u^3dA$$ and it plugged in equation of $$u_r$$ into integral.

My question is : We consider the $$\delta A$$ as area of annulus and find the integral with bound $$r\in [0,R]$$. which give the area of circle. I wonder what we call this small area $$\delta A$$ in math? Is this riemenn?

• $\delta A$ is the infinitesimal area enclosed between circles of radii $r$ and $r+\delta r$. Instead of differentiating, you might as well find it by $\delta A = \pi (r+\delta r)^2 - \pi r^2 = \pi (\delta r)^2 + 2\pi r\delta r \approx 2\pi r\delta r$. Here, we choose to neglect the higher order (second and larger) terms. – strawberry-sunshine Nov 22 at 8:45
• Also, yes, this is a Riemann sum. – strawberry-sunshine Nov 22 at 8:46
• @strawberry-sunshine . I understood. thank you very much for making it clear to me. – soheil Nov 22 at 8:50