**TI86** Program file dated 06/23/04, 19:57 Ä ´ZTHEOR4A´²àTo7ZINITo4ZLoŽD0/D0/-THE WORD 'ANTIDERIVITIVE' WILLoŽD7/D0/-BE 'A.D.' HERE. FINDING AN A.D.oŽD14/D0/-IS THE REVERSE OF DIFFERENTIATION.oŽD21/D0/-THE A.D. IS A family OF functions.oŽD32/D0/-ie. d/dt f=2t+1 dt=(2t^3)/3+t+A,oŽD39/D0/-WHERE 'A' CAN BE ANY CONSTANT.o4ZKoLD1/4MO/4T1/D2/4PR/3X/D4/4EX/3X/D5/4QU/3QoàT1oƒo4ZLoŽD0/D0/-REFER TO THE DERIVITIVE MENUoŽD7/D0/-FOR HELP IN FINDING AN A.D.,oŽD14/D0/-AND ALWAYS CHECK YOUR A.D.oŽD21/D0/-BY DIFFERENTIATING IT ORoŽD28/D0/-TESTING IT WITH THE EQUATIONoŽD35/D0/-EDITOR AND THE 'TABLE' AS FOLLOWS:o4ZKoLD1/4MO/4T2/D2/4PR/3T/D4/4EX/3X/D5/4QU/3QoàT2oƒo4ZLoŽD0/D0/-y1=your answeroŽD7/D0/-y2=der1(y1,x)oŽD14/D0/-y3=problemoŽD21/D0/-(un-SELECT y1) THEN Press [TABLE])oŽD28/D0/-TO NUMERICALLY CHECK FOR EQUALITY.o4ZKoLD1/4MO/4T3/D2/4PR/4T1/D4/4EX/3X/D5/4QU/3QoàT3oƒo4ZLoŽD0/D0/-THE ARC LENGTH OF f(x) IS:oD0 2xnD45 2yo4ZTo-A 4lbn-b 4lto5ZTLoŽD10/D13/-(1+(f'(x)))dxoŽD23/D0/-YOU WILL HAVE TO USE REIMANNoŽD29/D0/-SUMS TO FIND MOST A.D.s, OTHERWISEoŽD35/D0/-SEE ELEMENTARY A.D.s FOR EXAMPLES.o4ZKoLD1/4MO/4T4/D2/4PR/4T2/D4/4EX/3X/D5/4QU/3QoàT4oƒo4ZLoŽD0/D25/-CENTER OF MASSo6ZLINoŽD9/D0/-FOR n DISCRETE MASSES Mi, ONoŽD15/D0/-THE x-AXIS, EACH AT POSITION Xi,oŽD22/D0/-THE CENTER OF MASS IS THE POINT:oŽD30/D0/-Ë=(Æ XiMi)/ÆMi.oŽD37/D0/-XiMi IN THE NUMERATOR ARE momentso4ZKoLD1/4MO/4T5/D2/4PR/4T3/D4/4EX/3X/D5/4QU/3QoàT5oƒo4ZLoŽD0/D0/-OF THE MASSES Mi. THE DENOMINATORoŽD8/D0/-IS THE TOTAL MASS OF THE SYSTEM.oŽD16/D0/-IF THE SYSTEM IS ONE OBJECT ONoŽD24/D0/-THE x-AXIS BETWEEN x=A AND x=b,oŽD32/D0/-WITH MASS DENSITY ¿(x), THEN THEo4ZKoLD1/4MO/4T6/D2/4PR/4T4/D4/4EX/3X/D5/4QU/3QoàT6oƒo4ZLoŽD0/D0/-CENTER OF MASS IS:oD11 2xnD44 2yo4ZTo-A 4lbn-b 4lto5ZTLoŽD20/D0/-Ë=oŽD13/D22/-x¿(x)dxo–D11/D39/D50/D39oD11 2xnD27 2yo4ZTo-A 4lbn-b 4lto5ZTLoŽD30/D22/-¿(x)dxo4ZKoLD2/4PR/4T5/D4/4EX/3X/D5/4QU/3QoàQnD1 3KoàXoß