Integral Calculus Formula Sheet

Integral Calculus Formula Sheet Derivative Rules: 0dcdx 1nndxnxdx sincosdxxdx secsec tandxxxdx 2tansecdxxdx cossindxxdx csccsc cotdxxxdx 2cotcscdxxdx lnxxdaaadx xxdeedx ddcf xcf xdxdx dddf x gxf xgxdxdxdx fg f g fg 2fg fgfgg dfgxf gx gxdx Properties of Integrals: ()()kf u du k f u du () ()()()fu gu duf udugudu ()0aafxdx ()()baabfxdxf xdx ()()()cbcaabfxdxf xdxf xdx 1()baveaffxdxba 0()2 ()aaafxdxf xdx if f(x) is even ()0aafxdx if f(x) is odd ()()( ()) ()()fbbafagfx f xdxgudu udv uvvdu Integration Rules: du u C 11nnuuduCn lnduuCu uuedu e C 1lnuuadua Ca sincosuduu C cossinuduu C 2sectanuduu C 2csccotuuC csc cotcscuuduuC sec tansecuudu uC 221arctanduuCau aa 22arcsinduuCaau 221secuduarcCaauu a Fundamental Theorem of Calculus : ' xadFxftdtfxdx where ft is a continuous function on [a, x]. bafxdx Fb F a, where F(x) is any antiderivative of f(x). Riemann Sums: 11nniiiicaca 111nnniiiiiiiabab 1()lim()bnniafxdxf a i x x nabx 11nin 1(1)2ninni 21(1)(21)6ninnni 231(1)2ninni height of th rectanglewidth of th rectangleiii Right Endpoint Rule: ninabnabniiafxxiaf1)()(1)()()()( Left Endpoint Rule: ()()11((1))() ( )((1) )nnbabanniifa ix xfa i Midpoint Rule: (1)( )(1)( )2211()()()( )nniibaiibanniifax xfa Net Change: Displacement: ()bavxdx Distance Traveled: ()bavx dx 0()(0)( )tst svxdx 0()(0)( )tQt QQ xdx Trig

Fundamental Theorem of Calculus: x a d F xftdtfx dx where f t is a continuous function on [a, x]. b a f xdx Fb Fa, where F(x) is any antiderivative of f(x). Riemann Sums: 11 …

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