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Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by one petal of r=sin3θ

Short Answer

Expert verified

The area bounded by one petal isπ6unit2

Step by step solution

01

Given information

The curve isr=sin3θ

02

Area

The area bounded by the curve is,

A=12αβr2dθA=120π3sin3θ2dθA=120π3sin23θdθA=120π31-cos6θ2dθA=12θ-sin6θ60π3A=12π3-sin6π36-0A=π6unit2

The area of one petal isA=π6unit2

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