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Unformatted text preview: Formula Sheet for Final Exam Trig identities: sec x = 1 cos x csc x = 1 sin x cot x = cos x sin x cos 2 ( x ) = 1 + cos(2 x ) 2 sin 2 ( x ) = 1 cos(2 x ) 2 Integrals of trig functions: integraldisplay sec u du = ln | sec u +tan u | + C integraldisplay csc u du = ln | csc u cot u | + C Average value: Let f be continuous on [ a, b ]. The average value of f on [ a, b ] is f a ve = 1 b a integraldisplay b a f ( x ) dx. Area under a polar curve: Let R be the region bounded by the polar curve r = f ( ) and the rays = a and = b . Then Area R = integraldisplay b a 1 2 [ f ( )] 2 d. Complex numbers n th powers: If z = r (cos + i sin ), then for any integer n , z n = r n (cos( n ) + i sin( n )) . n th roots: For any integer n , the n th roots of r (cos + i sin ) are r 1 n parenleftbigg cos parenleftbigg + k 2 n parenrightbigg + i sin parenleftbigg + k 2 n parenrightbiggparenrightbigg , k = 0 , 1 . . ., n 1 ....
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This note was uploaded on 06/04/2008 for the course MATH 20B taught by Professor Justin during the Spring '08 term at UCSD.
- Spring '08