Question

In this section we described a method for approximating the area of a polar region bounded by two rays$\theta =\alpha$and $\theta =\beta$and a polar function $r=f\left(\theta \right)$The method involved a “subdivide, approximate, and add” strategy in which we fixed some general notation. Draw a carefully labeled picture that illustrates the roles of $∆\theta ,{{\theta }_k}^{*}$and $f({\theta }_k*)$for one approximating sector $S_k$.

Short answer

The required labeled picture is according to the given information is shown:

Step-by-step solution

Given information

Let the polar function is $r=f\left(\theta \right)$.

The objective is to draw a  labeled picture that illustrates the roles of ∆θ,θk*and f(θk*) for one approximating sector Sk.

According to the given information