   Chapter 10.4, Problem 1E

Chapter
Section
Textbook Problem

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

To determine

To Find: The area of the region that lies in the specified sector r=eθ4,π2θπ.

Explanation

Given:

The polar equation is r=eθ4 which tends to the range of angles θ between π2 and π.

Calculation:

Use the formula for the area as below.

A=ab12r2dθ=π/2π12(eθ/4)2dθ=12π/2π(e2θ/4)dθ=12π/2π(eθ/2)dθA=12[2eθ/2]π/2π

Apply the limits as below

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