Exam (elaborations) MA 2

The most important systems of units are shown in the table below. The mks system is also known as the International System of Units (abbreviated SI), and the abbreviations sec (instead of s), gm (instead of g), and nt (instead of N) are also used. System of units Length Mass Time Force cgs system centimeter (cm) gram (g) second (s) dyne mks system meter (m) kilogram (kg) second (s) newton (nt) Engineering system foot (ft) slug second (s) pound (lb) 1 inch (in.) 2.540000 cm 1 foot (ft) 12 in. 30.480000 cm 1 yard (yd) 3 ft 91.440000 cm 1 statute mile (mi) 5280 ft 1.609344 km 1 nautical mile 6080 ft 1.853184 km 1 acre 4840 yd2 4046.8564 m2 1 mi2 640 acres 2.5899881 km2 1 fluid ounce 1/128 U.S. gallon 231/128 in.3 29.573730 cm3 1 U.S. gallon 4 quarts (liq) 8 pints (liq) 128 fl oz 3785.4118 cm3 1 British Imperial and Canadian gallon 1.200949 U.S. gallons 4546.087 cm3 1 slug 14.59390 kg 1 pound (lb) 4.448444 nt 1 newton (nt) 105 dynes 1 British thermal unit (Btu) 1054.35 joules 1 joule 107 ergs 1 calorie (cal) 4.1840 joules 1 kilowatt-hour (kWh) 3414.4 Btu 3.6 • 106 joules 1 horsepower (hp) 2542.48 Btu/h 178.298 cal/sec 0.74570 kW 1 kilowatt (kW) 1000 watts 3414.43 Btu/h 238.662 cal/s °F °C • 1.8 32 1° 60 3600 0. radian For further details see, for example, D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics. 9th ed., Hoboken, N. J: Wiley, 2011. See also AN American National Standard, ASTM/IEEE Standard Metric Practice, Institute of Electrical and Electronics Engineers, Inc. (IEEE), 445 Hoes Lane, Piscataway, N. J. 08854, website at . 11/4/10 12:05 PM Page 2 Integration uv dx uv  uv dx (by parts) xn dx c (n  1) dx ln x c eax dx eax c sin x dx cos x c cos x dx sin x c tan x dx ln cos x c cot x dx ln sin x c sec x dx ln sec x tan x c csc x dx ln csc x  cot x c arctan c arcsin c arcsinh c arccosh c sin2 x dx _1 2 x  _1 4 sin 2x c cos2 x dx _1 2 x _1 4 sin 2x c tan2 x dx tan x  x c cot2 x dx cot x  x c ln x dx x ln x  x c eax sin bx dx (a sin bx  b cos bx) c eax cos bx dx (a cos bx b sin bx) c eax a2 b2 eax a2 b2 x a dx x2 a2  x a dx x2 a2  x a dx a2 x2  x a 1 a  dx x2 a2 1 a 1 x xn1 n 1 Differentiation (cu) cu (c constant) (u v) u v (uv) uv uv ( ) • (Chain rule) (xn) nxn1 (ex ) ex (eax) aeax (ax ) ax ln a (sin x) cos x (cos x) sin x (tan x) sec2 x (cot x) csc2 x (sinh x) cosh x (cosh x) sinh x (ln x) (loga x) (arcsin x) (arccos x)  (arctan x) (arccot x)  1 1 x2  1 1 x2 1 1x2  1 1x2   log