Q. 4. - Calculus

Question

When we investigated area in rectangular coordinates in Chapter $4$ we often tried to find the areas of regions under curves $y=f\left(x\right)$ from $x=a$ to $x=b$. In the polar plane, the typical region whose area we wish to find is a region R bounded by two rays $\theta =\alpha$and $\theta =\beta$ and a polar function of the form $r=f\left(\theta \right)$). Why is this our basic type of region in the polar plane?

Step-by-Step Solution

Answer

As a result, the basic region is defined as a region $R$ in the polar plane circumscribed by two rays$a=b$ and$c=d$

Step 1: Given information

The coordinates in a polar coordinate plane are indicated by $(r,\theta )$where $r$ denotes the distance from the origin and $\theta$ denotes the angle at which a ray goes clockwise or counterclockwise.

Step 2: Explain why is this our basic type of region in the polar plane?

We approximate a region with sectors of circles while working with polar coordinates.

As a result, the basic region is defined as a region $R$ in the polar plane circumscribed by two rays and $a=b$ and $c=d$