Double Integral One Loop of the Rose

[. Arctic.]

Homework Statement

Use a double integral to find the area of one loop of the rose r = cos 3$\theta$

Homework Equations

The Attempt at a Solution

This is a past test question. The only thing I got wrong was the set up while I got the rest of the mechanical steps right. I set up as

∫∫ (r*cos 3θ) dr dθ

which is not right. I thought it might either be

∫∫ (r*r) dr dθ

or

∫∫ (cos 3θ * cos 3θ) dr dθ

 

[SteamKing]

Hint: r = cos theta, emphasis on equal