I am having some problem with caluculating areas using double integrals in polar coordinates. The question is : Calculate the total area of the rose $ r = 5 \sin(2 \theta)$ using double integration in polar coordinates?
I took the limits of theta from $0$ to $\pi \over 4$ and that for $r$ from $0$ to $5 \sin(2 \theta)$ and multiplied it by $2$ to get the area of one petal of the rose and then multiplied it by 4 to get the total area.
My answer comes out to be $ 25 \pi \over 2$. Have I followed the right procedure and is the answer correct?