Pearson：Calulus（PPT讲稿）Chapter 5 Integration

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5.1 Approximating Areas under Curves 5.2 Definite Integrals 5.3 Fundamental Theorem of Calculus 5.4 Working with Integrals 5.5 Substitution Rule

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Chapter 5 Integration PEARSON Copyright @2011 Pearson Education, Inc. Publishing as Pears on Addis on-Wesley

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Chapter 5 Integration

5.1 Approximating Areas under Curves PEARSON Copyright @2011 Pearson Education, Inc. Publishing as Pears on Addis on-Wesley

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. 5.1 Approximating Areas under Curves

f(r) f(r) f(r)dx Slopes of tangent lines FIGURE 5.1 Copyright 2011 Pearson Education, Inc. Publishing as Pears on Addis on-Wesley Slide 5-4

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Slide 5 - 4

70 60 50 60 40 (velocity function) 30 20 10 0 0.5 1.0 2.0 Time(hr) FIGURE 5.2 Copyright 2011 Pearson Education, Inc. Publishing as Pears on Addis on-Wesley side5·5

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Slide 5 - 5

Elapsed time 70 2 h1 60 =60 50 40 Area displacement 30 Velocit (60 mi/hr)(2 hr) 120 =60 mi/hr 20 10 0. 1.01.52.0 Time(hr FIGURE 5.3 Copyright 2011 Pearson Education, Inc. Publishing as Pears on Addis on-Wesley Slide 5-6

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Slide 5 - 6

0000000 76543 50 0 n=8 FIGURE 5.4 Copyright 2011 Pearson Education, Inc. Publishing as Pears on Addis on-Wesley Slide 5-7

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Slide 5 - 7

70 60 40 30 20 10 345678 n=64 FIGURE 5.5 Copyright 2011 Pearson Education, Inc. Publishing as Pears on Addis on-Wesley Slide 5-8

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Slide 5 - 8

Table 5.1 Approximations to the area under the velocity curvev =t Approximation to Number of Leng gth of displacement subintervals each subinterval (area under curve) 28.0m 124 84 160.0m 168.0m 170.0m 0.5s 170.5m 32 0.25 170.625m 64 0.125s 170.65625m Copyright 2011 Pearson Education, Inc. Publishing as Pears on Addis on-Wesley Slide 5-9

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Slide 5 - 9

y=f(r) R FIGURE 5.6 Copyright 2011 Pearson Education, Inc. Publishing as Pears on Addis on-Wesley Slide 5-10

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Slide 5 - 10

FIGURE 5.7 Copyright 2011 Pearson Education, Inc. Publishing as Pears on Addis on-Wesley Slide5·11

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Slide 5 - 11

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