Integral of radical trigonometric functions revisited
  This article revisits an integral of radical trigonometric functions. It presents several methods of integration where the integrand takes the form $\sqrt{1 \pm \sin x}$ or $\sqrt{1 \pm \cos x}$. The integral has applications in Calculus where it appears as the length of cardioid represented in polar coordinates. 
N. Karjanto and B. Yermukanova
math.HO