UsefulRelations1

UsefulRelations1 - Useful Relations Pythagorean Identity:...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

This note was uploaded on 10/05/2011 for the course MATH 1272 taught by Professor Wilson during the Spring '08 term at Minnesota.

Ask a homework question - tutors are online