I am doing a question on finding the area enclosed by a loop, given by the equation:

$\displaystyle r = 2\cos^{\frac{3}{2}}\theta$ with $\displaystyle \frac{-\pi}{2} \le\theta\le \frac{\pi}{2}$.

I know that the area is $\displaystyle \frac{1}{2} \int r^2 d\theta$

Which works out to be $\displaystyle \frac{1}{2} \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} 4\cos^{3}\theta d\theta$

Taking out the 4 and expanding I end up with $\displaystyle 2 \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \cos{\theta}(1-\sin^{2}\theta) d\theta$

The book however has a 4 outside the brackets, is this a typo or something that I've missed?

Thanks for the help