Easy Integration Of Exponential Function

Integration of Exponential Function Presented by: Marc Cesar L. Pacilan BSED-3style.visibilityppt_xppt_ystyle.visibility “The essence of Mathematics is not to make simple things complicated but to make complicated things simple.” – Albert Einsteinstyle.visibilityppt_xppt_yppt_hppt_w One of the forms of functions is a power expression. That the variable is raised to a power and that power is called an exponent. However there are cases that a constant is raised to the variable power, that is, the variable acts as an exponent. Such a type of function is called an exponential function.style.visibility The process of integration is an inverse process of differentiation. Therefore an integral is an anti derivative of the function which we need to integrate. Keeping this in mind, we can solve integration of exponential functions.style.visibility Two Basic formulas for the Integration of Exponential Functions , style.visibilityppt_wppt_hppt_xppt_ystyle.visibilitystyle.rotationppt_xppt_ystyle.visibilitystyle.rotationppt_hppt_w As you do the following problems, remember these general rules for integration : style.visibilityppt_xppt_yppt_hppt_wstyle.visibilityppt_xppt_y Examples of integrating exponential functionsstyle.visibilityppt_wppt_xppt_yr 1.) style.visibilityppt_xppt_ystyle.visibilityppt_xppt_ystyle.visibilityppt_wppt_hppt_xppt_ystyle.visibilityppt_xppt_yppt_ystyle.visibilityppt_xppt_yppt_y 2.) style.visibilityppt_xppt_yppt_hppt_wstyle.visibilityppt_wppt_hstyle.rotationstyle.visibilityppt_wppt_hppt_xppt_ystyle.visibilityppt_xppt_ystyle.visibilityppt_xppt_yppt_yppt_yppt_y 3.) Use u-substitution. Let u = 2x+3 du = 2 dx , (1/2) du = dx . style.visibilityppt_xppt_ystyle.visibilityppt_xppt_ystyle.visibilitystyle.rotationppt_wppt_wppt_hppt_xppt_yppt_ystyle.visibilityppt_xppt_yppt_ystyle.visibilitystyle.rotationppt_xppt_yppt_xppt_ystyle.visibilityppt_xppt_yppt_hppt_wstyle.visibilityppt_xppt_y Substitute into the original problem, replacing all forms of x, getting style.visibilityppt_xppt_yppt_yppt_yppt_ystyle.visibilityppt_wppt_hppt_xppt_ystyle.visibilityppt_xppt_yppt_ystyle.visibilityppt_wppt_hppt_xppt_ystyle.visibilityppt_xppt_y 4.) Let u = cos 2x du = -2sin 2x dx dx= -1/2