730
Hypocyclic gears, 184, 402
Hypocycloids, 401-402
of four cusps, 292, 402, 423, 435,
628-683Identity matrix, 96
Implicit differentiation, 172, 176
Implicit functions, 172, 577
basic theorem on, 583-585
Improper integrals, 252
Income tax rates, 187
Increasing functions, 115, 294-313,
322, 328
Increments, 194, 562-563
Indefinite integrals, 202-212, 225
Independence of path, 658, 676
Independent vectors, 58
Indeterminate forms, 330-332
Induction (see Mathematical in-
duction)
Inequalities, 2-6, 35, 78, 441
elegant one, 504
exponential, 482
geometric mean <_ arithmetic
mean, 504
Schwarz, 78
triangle, 33
trigonometric, 441
Infinite decimals, 336-339
Infinite integrals (see Riemann-
Cauchy integrals)
Infinite series (see Series)
Infinitesimals, 144, 201, 250
Infinity, 134, 143-144, 592
Inflection (see Flexpoints)
Inner point, 293
Input (element of domain), 75,
114, 122
Instaneous rate (see Rates)
Integers, 5, 120, 319
Integrability, 216, 345-353, 609
Integral(s), 202
Archimedes, 349IndexIntegral(s), change of variable in,
221-223, 469-479
curve (or line), 426-428, 673-
676
derivatives of, 225, 573
of derivatives, 333, 659
double, 667-695
indefinite, 202-212, 225
iterated, 652-667
limits of, 350
modified Riemann, 223
multiple, 667-714
in polar coordinates, 687-695
Riemann, 214
Riemann-Cauchy, 250-256, 657,
667
Riemann-Stieltjes, 261, 276, 353
tables of, 205-206, end papers
of trigonometric functions, 205,
449-457
triple, 695-714
in cylindrical coordinates, 702-
707
in rectangular coordinates,
695-702
in spherical coordinates, 707-
714
of vector functions, 426
(See also Integration)
Integral test for convergence, 601-
603
Integrand, 203
Integration, formulas for, 205, end
papers
limits of, 214, 470
by partial fractions, 511-518
by parts, 210-211, 230, 328, 473,
477, 518-525, 633, 641, 655
by substitution, 469
by substitution z = tan (0/2),
477-479
technique for, 205-212
termwise, 620-621, 672
by trigonometric substitution,
471-474