Area of one loop of the curve $r=5\cos4\theta$
The area of one loop can be given by: $\frac{1}{2}\int^\frac{\pi}{8}_\frac{-\pi}{8}(5\cos4\theta)^2\,d\theta$. However this gives me an answer of $\frac{25}{8}\pi$ while the answer says its $\frac{25}{16}\pi$, why have I got double the area I should have calculated? Have I found the integral between the wrong values or is the answer for my question wrong? any help would be appreciated.