Q. 5. - Calculus

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 $S_k$.

Step-by-Step Solution

Answer

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

Step 1: Given information

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

Step 2: The objective is to draw a labeled picture that illustrates the roles of ∆ θ , θ k * and f ( θ k * ) for one approximating sector S k .

According to the given information