Lesson 9 Integration of Hyperbolic Functions

Lesson 9 - Click to edit Master subtitle style Integration of Hyperbolic TOPIC OBJECTIVES • identify the different hyperbolic functions • find

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Unformatted text preview: Click to edit Master subtitle style Integration of Hyperbolic TOPIC OBJECTIVES • identify the different hyperbolic functions; • find the integral of given hyperbolic functions; • determine the difference between the integrals of hyperbolic functions; and • evaluate integrals involving hyperbolic 2 sinh . 1 x x e e x-- = 2 cosh . 2 x x e e x- + = x x x x e e e e x x x-- +- = = cosh sinh tanh . 3 x x x x e e e e x x--- + = = tanh 1 coth . 4 x x e e x hx- + = = 2 cosh 1 sec . 5 x x e e x hx-- = = 2 sinh 1 csc . 6 Definitions : Differentiation Formulas ( 29 udu u d cosh sinh . 1 = ( 29 udu u d sinh cosh . 2 = ( 29 udu h u d 2 sec tanh . 3 = ( 29 udu h u d 2 csc coth . 4- = ( 29 udu hu hu d tanh sec sec . 5- = ( 29 udu coth hu csc hu csc d . 6- = . Note : The hyperbolic functions are defined in terms of the exponential functions. Its differentials may also be found by differentiating its equivalent exponential form. Similarly, the integrals of the hyperbolic functions can be derived by integrating the exponential form equivalent. Integration Formulas...
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This note was uploaded on 08/19/2011 for the course ECON 232 taught by Professor Charles during the Spring '11 term at MIT.

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Lesson 9 - Click to edit Master subtitle style Integration of Hyperbolic TOPIC OBJECTIVES • identify the different hyperbolic functions • find

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