
06655909
j
2016f.01159
Karjanto, Natanael
Yermukanova, Binur
Integral of radical trigonometric functions revisited.
Math. Enthus. 13, No. 3, 243254 (2016).
2016
Information Age Publishing (IAP), Charlotte, NC; University of Montana, Department of Mathematical Sciences, Missoula, MT
EN
I50
integral calculus
techniques of integration
radical trigonometric functions
integral of radical sine function
integral of radical sine function
rationalizing numerator
combining identities
twice trigonometric substitutions
variable shift
cardioids
length
http://scholarworks.umt.edu/tme/vol13/iss3/5
Summary: 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.