math cheat sheet

Math cheat sheet - b FTOC f x)dx = F(b − F(a a Trig Identities sin 2 θ cos 2 θ = 1 1 tan 2 θ = sec 2 θ sec 2 θ − 1 = tan 2 θ 1 sin 2

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FTOC: - = b a a F b F dx x f ) ( ) ( ) ( Anti-Derivatives C x x + - ) cos( ) sin( sec²(x)→ tan(x) + C sec(x) tan(x) → sec(x) + C C a a a x x + ln C x x + - ) cot( ) ( csc 2 C x x x + - ) csc( ) cot( ) csc( C x x + ) sec( ln ) tan( C x x + ) sin( ln ) cot( C a x a a x + + - 1 2 2 tan 1 1 C a x x a + - - 1 2 2 sin 1 Trig Identities 1 cos sin 2 2 = + θ 2 2 sec tan 1 = + 2 2 tan 1 sec = - )) 2 cos( 1 ( 2 1 sin 2 - = )) 2 cos( 1 ( 2 1 cos 2 + = Algebra 2 2 2 2 ) ( b ab a b a + + = + 2 2 2 2 ) ( b ab a b a + - = - ) ( ) )( ( 2 2 b a b a b a - = + - Trig Integrals xdx x b a cos sin Case 1 : b is odd 1. Save 1 cos(x) 2. Use x x 2 2 sin 1 cos - = to express remaining factors in terms of sin(x) 3. Let u = sin(x) Case 2: a is odd 1. Save 1 sin(x) 2. Use x x 2 2 cos 1 sin - = 3. Let u = cos(x) Case 3 1. Use half angle formula xdx x b a sec tan Case 1: b is even 1. save sec(x)
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This note was uploaded on 04/20/2008 for the course MATH 152 taught by Professor Wang during the Fall '07 term at WVU.

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Math cheat sheet - b FTOC f x)dx = F(b − F(a a Trig Identities sin 2 θ cos 2 θ = 1 1 tan 2 θ = sec 2 θ sec 2 θ − 1 = tan 2 θ 1 sin 2

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