   Chapter 10.4, Problem 4E

Chapter
Section
Textbook Problem

Find the area of the region that is bounded by the given curve and lies in the specified sector.4. r = 1/θ, π/2 ≤ θ ≤ 2π

To determine

To Find: The area of the region that lies in the specified sector r=1θ,π/2θ2π.

Explanation

Given:

The polar equation is r=1θ which tends to π/2θ2π.

Calculation:

Write the formula for area, A as below.

A=ab12r2dθ=π/22π12(1θ)2dθ=12π/22π1θ2dθ=12π/22πθ2dθ

A=12π/22πθ2dθ=12[θ2+12+1]π/

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