Useful Formulas

Useful Formulas - UsefulIntegrals udv = uv vdu e dx = e 1...

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ESE319 Useful Formulae Page 1 Useful Integrals udv = uv - vdu ∫∫ dx =ln(x) x xx edx=e 1 sin(ax)dx = - cos(ax) a 1 cos(ax)dx = sin(ax) a () dx 22 =ln x+ x a xa + + 3 22 2 2 dx x ax+ a = + x 1 dx -1 tan a a = + ⎛⎞ ⎜⎟ ⎝⎠ ax ax e e cos(bx)dx = acos(bx) + bsin(bx) a+b Trignometric Relations sin(x ± y) = sin(x)cos(y) ± cos(x)sin(y) cos(x ± y) = cos(x)cos(y) sin(x)sin(y) 2sin(x)sin(y) = cos(x - y) - cos(x + y) 2sin(x)cos(y) = sin(x + y) + sin(x + y) 2cos(x)cos(y) = cos(x + y) + cos(x - y) sin(2x) = 2sin(x)cos(x) 2 cos(2x) = cos (x) -sin (x) = 1- 2sin (x) sin(x) + sin(y) = 2sin cos x yx y +− sin(x) -sin(y) = 2cos sin x y cos(x) + cos(y) = 2cos cos x y cos(x) - cos(y) = 2sin sin x y o cos(x ± 90 ) = sin(x) o sin(x ± 90 ) = cos(x) ± sin(-x) = sin(x) cos(-x) = cos(x) jx e = cos(x) + jsin(x) jx -jx e+ e cos(x) =
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This note was uploaded on 02/24/2010 for the course ESE 319 taught by Professor Dhadwal during the Fall '08 term at SUNY Stony Brook.

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