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Calculus Cheat Sheet Integrals - Lamar University

Calculus Cheat Sheet Visit for a complete set of Calculus notes. 2005 Paul Dawkins Integrals Definitions Definite Integral: Suppose ()fx is continuous on [ ],ab. Divide [ ],ab into n subintervals of width x a nd choose *ix from each interval. Then ()()*1liminbanif x dxf xx == . Anti-Derivative : A n anti-derivative of ()fx is a function, ( )Fx, such that ( ) ( )F x fx =. Indefinite Integral :( )( )f x dxF xc=+ where ( )Fx is an anti-derivative of ( )fx. Fundamental Theorem of Calculus Part I : If ( )fx is continuous on [],ab then ( )( )xag xf t dt= is also continuous on [ ],ab and ( )( )()xadg xf t dtf xdx == . Part II : ( )fxis continuous on[ ],ab, ( )Fx is an anti-derivative of( )fx( ( )( )F xf x dx= ) then( )( )()baf x dxF bF a=.

Integration by Parts : ... and/or half angle formulas to reduce the integral into a form that can be integrated. For tan secnmx xdx we have the following : 1. n odd. Strip 1 tangent and 1 secant out and convert the rest to secants using tan sec 122xx= −, then use the substitution

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