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5 Integration 291 link
5.1 Sums and Sigma Notation 291 link
Evaluating Sums 293 link
5.2 Areas as Limits of Sums 296 link
The Basic Area Problem 297 link
Some Area Calculations 298 link
5.3 5.3.1 Määrätty integraali 302 kirja link
5.3.2 Jaot ja Riemannin summat 302 kirja link
5.3.3 Määrätty integraali 303 kirja link
5.3.4 Yleiset Riemannin summat 305 kirja link
5.3.5 Yleiset Riemannin summat, esimerkkejä 305 kirja link
5.4 Properties of the Definite Integral 307 link
A Mean-Value Theorem for Integrals 310 link
Definite Integrals of Piecewise Continuous Functions 311 link
5.5 The Fundamental Theorem of Calculus 313 link
5.6 The Method of Substitution 319 link
Trigonometric Integrals 323 link
5.7 Areas of Plane Regions 327 link
Areas Between Two Curves 328 link
Chapter Review 331 link

6 Techniques of Integration 334 link
6.1 Integration by Parts 334 link
Reduction Formulas 338 link
6.2 Integrals of Rational Functions 340 link
Linear and Quadratic Denominators 341 link
Partial Fractions 343 link
Completing the Square 345 link
Denominators with Repeated Factors 346 link
6.3 Inverse Substitutions 349 link
The Inverse Trigonometric Substitutions 349 link
Inverse Hyperbolic Substitutions 352 link
Other Inverse Substitutions 353 link
The tan(x/2) Substitution 354 link
6.4 Other Methods for Evaluating Integrals 356 link
The Method of Undetermined Coefficients 357 link
Using Maple for Integration 359 link
Using Integral Tables 360 link
Special Functions Arising from Integrals 361 link
6.5 Improper Integrals 363 link
Improper Integrals of Type I 363 link
Improper Integrals of Type II 365 link
Estimating Convergence and Divergence 368 link
6.6 The Trapezoid and Midpoint Rules 371 link
The Trapezoid Rule 372 link
The Midpoint Rule 374 link
Error Estimates 375 link
6.7 Simpson's Rule 378 link
6.8 Other Aspects of Approximate Integration 382 link
Approximating Improper Integrals 383 link
Using Taylor's Formula 383 link
Romberg Integration 384 link
The Importance of Higher-Order Methods 387 link
Other Methods 388 link
Chapter Review 389 link

7 Applications of Integration 393 link
7.1 Volumes by Slicing, Solids of Revolution 393 link
Volumes by Slicing 394 link
Solids of Revolution 395 link
Cylindrical Shells 398 link
7.2 More Volumes by Slicing 402 link
7.3 Arc Length and Surface Area 406 link
Arc Length 406 link
The Arc Length of the Graph of a Function 407 link
Areas of Surfaces of Revolution 410 link
7.4 Mass, Moments, and Centre of Mass 413 link
Mass and Density 413 link
Moments and Centres of Mass 416 link
Two- and Three-Dimensional Examples 417 link
7.5 Centroids 420 link
Pappus's Theorem 423 link
7.6 Other Physical Applications 425 link
Hydrostatic Pressure 426 link
Work 427 link
Potential Energy and Kinetic Energy 430 link
7.7 Applications in Business, Finance, and Ecology 432 link
The Present Value of a Stream of Payments 433 link
The Economics of Exploiting Renewable Resources 433 link
7.8 Probability 436 link
Discrete Random Variables 437 link
Expectation, Mean, Variance, and Standard Deviation 438 link
Continuous Random Variables 440 link
The Normal Distribution 444 link
Heavy Tails 447 link
7.9 First-Order Differential Equations 450 link
Separable Equations 450 link
First-Order Linear Equations 454 link
Chapter Review 458 link