   Chapter 10.5, Problem 80E

Chapter
Section
Textbook Problem

# Logarithmic Spiral The curve represented by the equation r = a e b θ , where a and b are constants, is called a logarithmic spiral. The figure shows the graph of r = e θ / 6 , − 2 π ≤ θ ≤ 2 π . Find the area of the shaded region. To determine

To Calculate: The area of the shaded region.

Explanation

Given:

The curve represented by the equation r=aebθ; where a and b constants called logarithmic spiral the figures displayed in the graph of r=eθ6 and 2πθ2π.

Formula Used:

A=12αβ[f(θ)]2dθ

Calculation:

Area of spiral curve in the interval 2πθ2π will be

A=122π2πr2dθ

=122π2π(eθ6)2dθ

=122π2π

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