Page 296 - Calculus Workbook For Dummies

280 Calculus Workbook For Dummies

inflection points functions, average value of, 219–220
curves, 102–105 irregular solids, 222–226
second derivative test, 270 meat slicer method, 222–226
integral comparison test, 247–250 by parts. See also product rule
integrals definition, 193
arc length, 227–228 expressions with trigonometric functions,
area calculation, 227–228 196–198
areas between curves, 220–221, 274 LIATE mnemonic, 193
average value of functions, 219–220 partial fractions, 201–204
cylindrical shell method, 222–226 problems, 194–204
definite, 166–167, 274 Pythagorean Theorem, 198–201
disk/washer method, 222–226 selecting a function, 193–196
improper, 231–233 SohCahToa right triangle, 198–201
indefinite, 179–182, 274 solutions, 205–216
infinite limit of, 231–233 trigonometric substitution, 198–201
irregular solids, 222–226 problems, 220–233
length along a function, 227–228 solutions, 234–242
meat slicer method, 222–226 volumes, 222–226
problems, 220–233
solutions, 234–242 • K •
surface of revolution, 227–228
volume calculation, 222–226 Kasube, Herbert, 193
integrands, 166
integration • L •
arc length, 227–228
areas. See also antiderivatives least-common-denominator method, 40–43
approximating, 159–161, 168–170 L’Hôpital’s rule, 229–231
below the x-axis, 275 LIATE mnemonic, 193
chunking, 275 limit comparison test, 247–250
under a curve, 159–161, 168–170, 274–275 limit problems
definite integral, 166–167 horizontal asymptote, 47
exact areas, 166 limits at infinity, 47–49
index of summation, 162 rational functions, 47
infinite limits of, 231–233 solutions, 50–56
integrands, 166 solving with
irregular shapes, 159–161 algebra, 39–43
length along a function, 227–228 calculator, 44–45
long sums, shorthand for, 162–166 canceling method, 40–43
midpoint rule, 273 conjugate multiplication method, 40–43
problems, 160–170, 220–233 factoring method, 40–43
rectangles, 159–161 FOILing method, 40–43
Reimann sums, 162–166 least common denominator method, 40–43
sigma notation, 162–166 L’Hôpital’s rule, 229–231
Simpson’s rule, 168–170, 273–274 sandwich method, 46–47
solutions, 171–176, 234–242 simplification method, 40–43
surface of revolution, 227–228 squeeze method, 46–47
Trapezoid rule, 168–170, 273 types of expressions, 48–49
triangles, 12 limits
between curves, 220–221, 274 13231 mnemonic, 267
cylindrical shell method, 222–226 33333 mnemonic, 265–266
disk/washer method, 222–226 definition, 31–32