   Chapter 10.4, Problem 2E

Chapter
Section
Textbook Problem

1–4 Find the area of the region that is bounded by the given curve and lies in the specified sector. r = cos θ , 0 ≤ θ ≤ π / 6

To determine

To find:

The area of the region that lies in the specified sector 0θπ6

and is bounded by the given curve r=cosθ

Explanation

1) Concept:

For the polar region , the formula for the area A is

A= ab12 r2 dθ

2) Given:

The region is bounded by the curve r=cosθ and lies in the sector

0θπ6

3) Calculation:

Given that the region is bounded by the curve r=cosθ and lies in the sector 0θπ6

By using concept,

A=0π612 r2 dθ

A=0π612 (cosθ)2 dθ

=120π6cos2θ dθ

A=120π612 1+cos2θdθ

……….

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