To find the area of one petal of r=cos 3 theta, integrate the equation over an interval that covers one complete petal, which is from 0 to 2pi/3. Simplify and evaluate the integral to find the exact area of one petal.
To find the area of one petal of r = cos 3 theta, we can start by understanding the polar equation r = cos 3 theta. The equation represents a rose curve with 3 petals. Each petal is symmetric, so we can find the area of one petal and multiply it by 3 to get the total area of the rose curve.
The area of one petal can be found by integrating the equation r = cos 3 theta over an interval that covers one complete petal. The interval can be determined by setting theta such that the equation goes from 0 to 2pi/3. The integral will give us the area of one petal.
After integrating, we can simplify the expression and evaluate it to find the exact area of one petal.