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Prove that the area enclosed by all of the petals of the polar rose r = cos 2nθ is the same for every positive integer n.

Short Answer

Expert verified

It is proved that area enclosed by all of the petals of the given polar rose is equal for every positive integer n.

Step by step solution

01

Step 1. Given information

Equation of petal rose isr=cos2nθ

02

Step 2. Explanation

Area =2n202πncos2nθ2dθ

=n02πn1+cos4nθ2dθ=n2π2n+sin4n2πn2(4n)-0=n2π2n+0=π

So, the area enclosed by all of the petals of the polar rose r = cos 2nθ is the same for every positive integer n.

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