Chapter 6 | Applications of Integration
745
6.9 | Calculus of the Hyperbolic Functions Learning Objectives 6.9.1 Apply the formulas for derivatives and integrals of the hyperbolic functions. 6.9.2 Apply the formulas for the derivatives of the inverse hyperbolic functions and their associated integrals. 6.9.3 Describe the common applied conditions of a catenary curve. We were introduced to hyperbolic functions in Introduction to Functions and Graphs , along with some of their basic properties. In this section, we look at differentiation and integration formulas for the hyperbolic functions and their inverses. Derivatives and Integrals of the Hyperbolic Functions Recall that the hyperbolic sine and hyperbolic cosine are defined as sinh x = e x − e − x 2 andcosh x = e x + e − x 2 . The other hyperbolic functions are then defined in terms of sinh x and cosh x . The graphs of the hyperbolic functions are shown in the following figure.
Figure 6.81 Graphs of the hyperbolic functions.
It is easy to develop differentiation formulas for the hyperbolic functions. For example, looking at sinh x we have
Made with FlippingBook - professional solution for displaying marketing and sales documents online