Math Midterm Cheat - M x f ≀ K x f ≀ 4 4 2 4 3 3 2 1 n n b a x f x f x f x f x f x S dx x f βˆ† = β‰ˆ ∠2 3 12 n a b M E n-≀ Trapezoidal 2 3

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Integration Formulas = x dx x ln 1 = a a dx a x x ln - = x xdx cot csc 2 = x xdx tan sec 2 = x xdx x sec tan sec - = x xdx x csc cot csc + = x x xdx tan sec ln sec - = x x xdx cot csc ln csc = x xdx sec ln tan = x xdx sin ln cot = + - a x a a x dx 1 2 2 tan 1 = - - a x x a dx 1 2 2 sin Fundamental Theorem of Calculus = - = b a a f b f dx x f ) ( ) ( ) ( ' ) ( ) ( ' x f x F = Arc Length = dx x f b a + 2 ) ( ' 1 Integration By Parts - = vdu uv udv sin(x+y) = sin(x)cos(y) + cos(x)sin(y) sin(x-y) = sin(x)cos(y) - cos(x)sin(y) Trig Identities sin 2 x + cos 2 x = 1 2 ) 2 cos( 1 sin 2 x x - = tan 2 x + 1 = sec 2 x 2 ) 2 cos( 1 cos 2 x x + = 1 + cot 2 x = csc 2 x ) 2 cos( 1 ) 2 cos( 1 tan 2 x x x + - = Error Bound
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Unformatted text preview: M x f ≀ ) ( ' ' K x f ≀ ) ( ) 4 ( [ ] ) ( ... ) ( 4 ) ( 2 ) ( 4 ) ( 3 ) ( 3 2 1 n n b a x f x f x f x f x f x S dx x f + + + + + βˆ† = β‰ˆ ∫ 2 3 12 ) ( n a b M E n-≀ Trapezoidal 2 3 24 ) ( n a b M E n-≀ Midpoint 4 5 180 ) ( n a b K E n-≀ Simpson’s Improper Integrals } , 1 , 1 { divergent p convergent p x dx a p ≀ = ∫ ∞...
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This note was uploaded on 04/01/2008 for the course MATH 1B taught by Professor Reshetiken during the Fall '08 term at University of California, Berkeley.

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