FORMULA SHEET (TEST #1) Some identities 1. cos2(x) + sin2(x)=1
Transcription
FORMULA SHEET (TEST #1) Some identities 1. cos2(x) + sin2(x)=1
FORMULA SHEET (TEST #1) Some identities 1. cos2 (x) + sin2 (x) = 1 1 + cos(2x) 2 1 − cos(2x) 3. sin2 (x) = 2 2. cos2 (x) = 4. cosh2 (x) − sinh2 (x) = 1 cosh(2x) + 1 2 cosh(2x) −1 6. sinh2 (x) = 2 5. cosh2 (x) = Inverse Trigonometric Integral Identities ! du u √ 1. = sin−1 ( ) + C, u2 < a2 a a2 − u2 ! du 1 u 2. = tan−1 ( ) + C a2 + u2 a a " " ! " " du 1 −1 " u " √ 3. = sec " " + C, u2 > a2 2 2 a a u u −a Inverse Hyperbolic-Trig Integral Identities ! du u √ 1. = sinh−1 ( ) + C, a > 0 a a2 + u2 ! du u √ 2. = cosh−1 ( ) + C, u > a > 0 a u2 − a2 ! du 1 u 3. = tanh−1 ( ) + C, if u2 < a2 a2 − u2 a a ! du 1 u 4. = coth−1 ( ) + C, if u2 > a2 a2 − u2 a a ! du 1 u √ 5. = − sech−1 ( ) + C, 0 < u < a 2 2 a a u a −u " " ! "u" du 1 √ 6. = − csch−1 "" "" + C, u #= 0 2 2 a a u a +u Moments, Mass and Center of Mass of a Thin Rod along x-axis ! b ! b MO Mass: M = δ(x)dx Moments: MO = xδ(x)dx Center of Mass: x̄ = M a a Moments, Mass and Center of Mass of a Thin Plate ! ! ! Mass: M = dm Moments: Mx = ỹ dm, My = x̃ dm Center of Mass: x̄ = My Mx , ȳ = M M