Find the Area in polar coordinates

[MozAngeles]

Homework Statement

I am doing even problems in my book to study and i want to check this answer to see if it is right.
q: Find the area enclosed by one leaf of the three-leaved rose r=sin3(theta)

Homework Equations

A= integral 1/2 r² d(theta)

The Attempt at a Solution

i used the formula setting the limits from 0 to pi/3 i got my answer to be pi/12 is this right?

 

[mahdisadjadi]

Yes, your answer is correct:

$$A=\frac{1}{2}\int\limits_{0}^{\frac{\pi}{3}}<br /> [sin(3\theta)]^{2} d\theta = \frac{\pi}{12}$$