Part II : ( )fxis continuous on,ab, ( )Fx is an anti-derivative of( )fx( ( )( )F xf x dx= ) then( )( )()baf x dxF bF a=.Ģ Variants of Part I : ()( )()()uxadf t dtu x f u xdx = ( )( )( )( )bvxdf t dtv x f v xdx = ( )( )( )( )( )()()uxvxuxvxdftdt u xfv xfdx = Properties ( ) ( )( )( )f xg x dxf x dxg x dx = ( ) ( )( )()bbbaaaf xg x dxf x dxg x dx = ()0aaf x dx= ( )( )baabf x dxf x dx= ( )( )cf x dxc f x dx=, c is a constant ()()bbaacf x dxcf x dx=, c is a constant ()bac dxc b a= ( )( )bbaaf x dxf x dx ( )( )( )b cba acf x dxf x dxf x dx=+ for any value of c. 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 =. Indefinite Integral :( )( )f x dxF xc=+ where ( )Fx is an anti-derivative of ( )fx. Anti-Derivative : A n anti-derivative of ()fx is a function, ( )Fx, such that ( ) ( )F x fx =. Divide ,ab into n subintervals of width x a nd choose *ix from each interval.

2005 Paul Dawkins Integrals Definitions Definite Integral: Suppose ()fx is continuous on ,ab. 1 Calculus Cheat Sheet Visit for a complete set of Calculus notes.