This article revisits an integral of radical trigonometric functions. It presents several methods of integration where the integrand takes the form 1+/- sin x or 1+/- cos x. The integral has applications in Calculus where it appears as the length of cardioid represented in polar coordinates.
Karjanto, Natanael and Yermukanova, Binur
"Integral of radical trigonometric functions revisited,"
The Mathematics Enthusiast: Vol. 13
, Article 5.
Available at: http://scholarworks.umt.edu/tme/vol13/iss3/5