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Chapter 15 Multiple Integrals

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Presentation on theme: "Chapter 15 Multiple Integrals"— Presentation transcript:

1

2 Chapter 15 Multiple Integrals
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

3 15.1 Double Integrals Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

4 Copyright © 2008 Pearson Education, Inc
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5 Copyright © 2008 Pearson Education, Inc
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9 Copyright © 2008 Pearson Education, Inc
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11 Copyright © 2008 Pearson Education, Inc
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12 Copyright © 2008 Pearson Education, Inc
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13 Copyright © 2008 Pearson Education, Inc
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14 Copyright © 2008 Pearson Education, Inc
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15 Copyright © 2008 Pearson Education, Inc
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16 Copyright © 2008 Pearson Education, Inc
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17 Copyright © 2008 Pearson Education, Inc
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19 Copyright © 2008 Pearson Education, Inc
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20 Copyright © 2008 Pearson Education, Inc
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21 Copyright © 2008 Pearson Education, Inc
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22 Copyright © 2008 Pearson Education, Inc
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23 Copyright © 2008 Pearson Education, Inc
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24 Area, Moments, and Centers of Mass
15.2 Area, Moments, and Centers of Mass Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

25 Copyright © 2008 Pearson Education, Inc
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26 Copyright © 2008 Pearson Education, Inc
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27 Copyright © 2008 Pearson Education, Inc
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28 Copyright © 2008 Pearson Education, Inc
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29 Copyright © 2008 Pearson Education, Inc
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30 Copyright © 2008 Pearson Education, Inc
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31 Copyright © 2008 Pearson Education, Inc
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32 Copyright © 2008 Pearson Education, Inc
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33 Copyright © 2008 Pearson Education, Inc
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34 Copyright © 2008 Pearson Education, Inc
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35 Copyright © 2008 Pearson Education, Inc
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36 Copyright © 2008 Pearson Education, Inc
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37 Copyright © 2008 Pearson Education, Inc
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38 Double Integrals in Polar Form
15.3 Double Integrals in Polar Form Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

39 Copyright © 2008 Pearson Education, Inc
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40 Copyright © 2008 Pearson Education, Inc
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41 Copyright © 2008 Pearson Education, Inc
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42 Copyright © 2008 Pearson Education, Inc
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43 Copyright © 2008 Pearson Education, Inc
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44 Copyright © 2008 Pearson Education, Inc
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45 Copyright © 2008 Pearson Education, Inc
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46 Copyright © 2008 Pearson Education, Inc
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47 Triple Integrals in Rectangular Coordinates
15.4 Triple Integrals in Rectangular Coordinates Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

48 Copyright © 2008 Pearson Education, Inc
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49 Copyright © 2008 Pearson Education, Inc
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50 Copyright © 2008 Pearson Education, Inc
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51 Copyright © 2008 Pearson Education, Inc
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52 Copyright © 2008 Pearson Education, Inc
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53 Copyright © 2008 Pearson Education, Inc
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54 Continued on next slide
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55 Copyright © 2008 Pearson Education, Inc
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56 Copyright © 2008 Pearson Education, Inc
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57 Copyright © 2008 Pearson Education, Inc
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58 Masses and Moments in Three Dimensions
15.5 Masses and Moments in Three Dimensions Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

59 Copyright © 2008 Pearson Education, Inc
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60 Copyright © 2008 Pearson Education, Inc
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61 Copyright © 2008 Pearson Education, Inc
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62 Copyright © 2008 Pearson Education, Inc
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63 Copyright © 2008 Pearson Education, Inc
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64 Copyright © 2008 Pearson Education, Inc
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65 Copyright © 2008 Pearson Education, Inc
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66 Triple Integrals in Cylindrical and Spherical Coordinates
15.6 Triple Integrals in Cylindrical and Spherical Coordinates Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

67 Copyright © 2008 Pearson Education, Inc
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68 Copyright © 2008 Pearson Education, Inc
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69 Copyright © 2008 Pearson Education, Inc
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70 Copyright © 2008 Pearson Education, Inc
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71 Copyright © 2008 Pearson Education, Inc
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72 Copyright © 2008 Pearson Education, Inc
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73 Copyright © 2008 Pearson Education, Inc
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74 Copyright © 2008 Pearson Education, Inc
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76 Copyright © 2008 Pearson Education, Inc
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77 Copyright © 2008 Pearson Education, Inc
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78 Copyright © 2008 Pearson Education, Inc
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79 Copyright © 2008 Pearson Education, Inc
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80 Copyright © 2008 Pearson Education, Inc
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81 Copyright © 2008 Pearson Education, Inc
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82 Copyright © 2008 Pearson Education, Inc
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83 Substitutions in Multiple Integrals
15.7 Substitutions in Multiple Integrals Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

84 Copyright © 2008 Pearson Education, Inc
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85 Copyright © 2008 Pearson Education, Inc
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86 Copyright © 2008 Pearson Education, Inc
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90 Copyright © 2008 Pearson Education, Inc
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91 Copyright © 2008 Pearson Education, Inc
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92 Copyright © 2008 Pearson Education, Inc
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