| 5 | Integrointi | 291 |
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| 5.0’ | Johdanto | 293 | | html | pdf
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| 5.0.1 | Antiderivaatta | 293 | | html | pdf
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| 5.0.2 | Integroimiskaavat saadaan derivoimiskaavoista | 293 | | html | pdf
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| 5.0.3. | Differentiaaliyhtälö | 293 | | html | pdf
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| 5.1 | Summat ja sigma-merkintä | 291 |
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| 5.1.1 | Summat ja sigma-merkintä | 293 | | html | pdf
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| 5.1.2 | Summat ja sigma-merkintä, jatkuu | 293 | | html | pdf
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| 5.1.3 | Summien ominaisuuksia | 293 | | html | pdf
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| 5.1.4 | Summakaavoja | 293 | | html | pdf
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| 5.2 | Pinta-alat summien raja-arvona | 296 |
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| 5.2.1 | Pinta-ala-ongelma | 296 | | html | pdf
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| 5.2.2 | Pinta-ala-ongelman ratkaisu | 296 | | html | pdf
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| 5.2.3 | Tasavälinen jako | 296 | | html | pdf
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| 5.2.4 | Summan raja-arvon laskeminen | 296 | | html | pdf
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| 5.3 | Määrätty integraali | 302 |
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| 5.3.1 | Määrätty integraali | 302 | | html | pdf
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| 5.3.2 | Jaot ja Riemannin summat | 302 | | html | pdf
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| 5.3.3 | Määrätty integraali | 303 | | html | pdf
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| 5.3.4 | Yleiset Riemannin summat | 305 | | html | pdf
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| 5.3.5 | Yleiset Riemannin summat, esimerkkejä | 305 | | html | pdf
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| 5.4 | Määrätyn integraalin ominaisuuksia | 307 |
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| 5.4.1 | Integrointirajat ja lineaarisuus | 310 | | html | pdf
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| 5.4.2 | Arvioita sekä parillinen ja pariton funktio | 310 | | html | pdf
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| 5.4.3 | Integraalilaskennan väliarvolause | 310 | | html | pdf
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| 5.4.4 | Integraalilaskennan väliarvolause, todistus | 310 | | html | pdf
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| 5.4.5 | Paloittain jatkuvat funktiot | 311 | | html | pdf
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| 5.5 | Analyysin peruslause | 313 |
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| 5.5.1 | Analyysin peruslause | 313 | | html | pdf
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| 5.5.2 | Analyysin peruslause, todistus | 313 | | html | pdf
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| 5.5.3 | Merkintöjä | 313 | | html | pdf
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| 5.5.4 | Analyysin peruslause, esimerkkejä | 313 | | html | pdf
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| 5.5.5 | Analyysin peruslause, esimerkkejä2 | 313 | | html | pdf
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| 5.5.6 | Analyysin peruslause, esimerkkejä3 | 313 | | html | pdf
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| 5.5.7 | Leibnitzin integraalisääntö | 313 | | html | pdf
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| 5.6 | The Method of Substitution | 319 |
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| | Trigonometric Integrals | 323 |
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| 5.7 | Areas of Plane Regions | 327 |
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| | Areas Between Two Curves | 328 |
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| | Chapter Review | 331 |
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| 6 | Techniques of Integration | 334 |
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| 6.1 | Integration by Parts | 334 |
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| | Reduction Formulas | 338 |
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| 6.2 | Integrals of Rational Functions | 340 |
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| | Linear and Quadratic Denominators | 341 |
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| | Partial Fractions | 343 |
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| | Completing the Square | 345 |
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| | Denominators with Repeated Factors | 346 |
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| 6.3 | Inverse Substitutions | 349 |
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| | The Inverse Trigonometric Substitutions | 349 |
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| | Inverse Hyperbolic Substitutions | 352 |
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| | Other Inverse Substitutions | 353 |
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| | The tan(x/2) Substitution | 354 |
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| 6.4 | Other Methods for Evaluating Integrals | 356 |
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| | The Method of Undetermined Coefficients | 357 |
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| | Using Maple for Integration | 359 |
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| | Using Integral Tables | 360 |
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| | Special Functions Arising from Integrals | 361 |
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| 6.5 | Improper Integrals | 363 |
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| | Improper Integrals of Type I | 363 |
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| | Improper Integrals of Type II | 365 |
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| | Estimating Convergence and Divergence | 368 |
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| 6.6 | The Trapezoid and Midpoint Rules | 371 |
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| | The Trapezoid Rule | 372 |
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| | The Midpoint Rule | 374 |
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| | Error Estimates | 375 |
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| 6.7 | Simpson's Rule | 378 |
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| 6.8 | Other Aspects of Approximate Integration | 382 |
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| | Approximating Improper Integrals | 383 |
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| | Using Taylor's Formula | 383 |
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| | Romberg Integration | 384 |
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| | The Importance of Higher-Order Methods | 387 |
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| | Other Methods | 388 |
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| | Chapter Review | 389 |
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| 7 | Applications of Integration | 393 |
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| 7.1 | Volumes by Slicing, Solids of Revolution | 393 |
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| | Volumes by Slicing | 394 |
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| | Solids of Revolution | 395 |
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| | Cylindrical Shells | 398 |
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| 7.2 | More Volumes by Slicing | 402 |
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| 7.3 | Arc Length and Surface Area | 406 |
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| | Arc Length | 406 |
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| | The Arc Length of the Graph of a Function | 407 |
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| | Areas of Surfaces of Revolution | 410 |
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| 7.4 | Mass, Moments, and Centre of Mass | 413 |
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| | Mass and Density | 413 |
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| | Moments and Centres of Mass | 416 |
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| | Two- and Three-Dimensional Examples | 417 |
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| 7.5 | Centroids | 420 |
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| | Pappus's Theorem | 423 |
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| 7.6 | Other Physical Applications | 425 |
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| | Hydrostatic Pressure | 426 |
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| | Work | 427 |
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| | Potential Energy and Kinetic Energy | 430 |
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| 7.7 | Applications in Business, Finance, and Ecology | 432 |
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| | The Present Value of a Stream of Payments | 433 |
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| | The Economics of Exploiting Renewable Resources | 433 |
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| 7.8 | Probability | 436 |
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| | Discrete Random Variables | 437 |
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| | Expectation, Mean, Variance, and Standard Deviation | 438 |
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| | Continuous Random Variables | 440 |
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| | The Normal Distribution | 444 |
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| | Heavy Tails | 447 |
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| 7.9 | First-Order Differential Equations | 450 |
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| | Separable Equations | 450 |
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| | First-Order Linear Equations | 454 |
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| | Chapter Review | 458 |
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