Excerpt from The Calculus (Revised): An Elementary Treatise on the Differential and Integral Calculus, With Practical Applications, Prepared for the Use of the Midshipmen of the United States Naval AcademyIndefinite integrals of powers of trigonometric functions. Definite integral as the limit of a sum Element of integration and application to problems.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.