Arc length of y=f(x): Exercises bank with detailed step-by-step solutions

This compilation contains exercises and their detailed step-by-step solutions on the calculation of curve arc lengths defined by Cartesian equations y=f(x)..It is intended for students who are taking an Integral Calculus course for the first time.

Calculate the length of an arc of a curve y=f(x) requires the calculation of the indefinite integral ∫√(1+(f′(x))²)dx. The presence of the radical complicates the task of finding an anti derivative. Unlike the other chapters of the integral calculus, where a large number of exercises can be found in textbooks, it can be said without exaggeration that there is a shortage of exercises for calculation of arc lengths.

In this book, a great number of exercises are compiled on the calculation of arc lengths. There are examples of all the classical types found in the most popular books of integral calculus nowadays, such as those by G. B. Thomas, (13th Ed., 2014), R. Larson, (10th Ed, 2014), H. Anton, (10th Ed, 2012), J. Stewart (8th Ed. 2015) to mention just a few. There are also several examples which appear for the first time in this book. There are more than 130 calculations of arc lengths, all made step-by-step with every detail.
The author hope that with this book he would have filled a gap in literature.