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Unformatted text preview: Useful Relations
Pythagorean Identity: "trig-squares identities": sin2 x + cos 2 x = 1 tan 2 x + 1 = sec 2 x 1 + cot 2 x = csc 2 x some derivatives: sin 2 x = 1 (1 - cos 2x) 2 2 cos x = 1 (1 + cos 2x) 2 d (cot x) = - csc 2 x dx
d (csc x) = - csc x cot x dx d (tan x) = sec 2 x dx
d (sec x) = sec x tan x dx
d (sin-1 x) = dx 1 1- x 2 d 1 (cos-1 x) = - dx 1- x 2 d 1 (tan-1 x) = dx 1 + x2 some integrals: tan x dx sec x dx = ln sec x + C = ln sec x + tan x + C cot x dx = ln sin x + C csc x dx
ds = dx 2 + dy 2 = ln csc x - cot x + C infinitesimal arclength element: S = generic surface area integral for solid of revolution: moment integrals: b a 2 r ds ( r is measured from axis of rotation ) My = b a x f (x) dx Mx = b a (moment about function's axis) (moment about variable's axis) 1 [ f (x) ]2 dx 2 ...
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This note was uploaded on 10/05/2011 for the course MATH 1272 taught by Professor Wilson during the Spring '08 term at Minnesota.
- Spring '08