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).

Net Change: Displacement: b a vxdx Distance Traveled: b a vx dx 0 (0) ( ) t st s vxdx 0 (0) ( ) t Qt Q Q xdx Trig Formulas: 2 1 sin ( ) 1 cos(2 )x 2 sin tan cos x x x 1 sec cos x x cos( ) cos( ) x x 22sin ( ) cos ( ) 1xx 2 1 cos ( ) 1 cos(2 )x 2 cos cot sin x x x 1 csc sin x x

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  Displacement

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