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Prove that the part of the polar curve r=1θthat lies inside the circle defined by the polar equation r = 1 has infinite length.

Short Answer

Expert verified

It is proved that the part of the polar curve that lies inside the circle defined by the polar equation r = 1 has infinite length.

Step by step solution

01

Step 1. Given information

An equation of a polar curve isr=1θ

02

Step 2. Explanation

Length =11θ4+1θ2dθ

=11+θ2θ4dθ=sinh-1θ-1+θ2θ1=sinh-1-1+2-sinh-11+1+121=

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