Calculus Cheat Sheet.pdf

# 7 13 4 4 3 16 a b c b a c a b c an alternate method

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7 13 4 0 4 3 16 A B C B A C A B C + = = = = = = An alternate method that sometimes works to find constants. Start with setting numerators equal in previous example : ( ) ( ) ( ) 2 2 7 13 4 1 x x A x Bx C x + = + + + . Chose nice values of x and plug in. For example if 1 x = we get 20 5 A = which gives 4 A = . This won’t always work easily.

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Calculus Cheat Sheet Visit for a complete set of Calculus notes. © 2005 Paul Dawkins Work : If a force of ( ) F x moves an object in a x b , the work done is ( ) b a W F x dx = Average Function Value : The average value of ( ) f x on a x b is ( ) 1 b avg a b a f f x dx = Arc Length Surface Area : Note that this is often a Calc II topic. The three basic formulas are, b a L ds = 2 b a SA y ds π = (rotate about x -axis) 2 b a SA x ds π = (rotate about y -axis) where ds is dependent upon the form of the function being worked with as follows. ( ) ( ) 2 1 if , dy dx ds dx y f x a x b = + = ( ) ( ) 2 1 if , dx dy ds dy x f y a y b = + = ( ) ( ) ( ) ( ) 2 2 if , , dy dx dt dt ds dt x f t y g t a t b = + = = ( ) ( ) 2 2 if , dr d ds r d r f a b θ θ θ θ = + = With surface area you may have to substitute in for the x or y depending on your choice of ds to match the differential in the ds . With parametric and polar you will always need to substitute.
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