CH 5

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CH 5

• Integration
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• Area and Distance
• The Definite Integral
• The Fundamental Theorem of Calculus
• Indefinite Integrals and the Net Change Theorem
• Tne Substitution Rule

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5.1

• Area and Distance
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YES
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Example 1

• Use rectangles to estimate the area under the
  parabola y x2 from 0 to 1, the parabolic
  region S illustrated here.

Figure 5.1.3, p. 289
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0.21875 lt A lt 0.46875
Figure 5.1.5, p. 290
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0.2734375 lt A lt 0.3984375
Figure 5.1.6, p. 290
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Figure 5.1.8, p. 292
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• ???????,??x (b-a)/n
• ????????x??, xi a i ?x
• ???????????, f(xi)
• ???????????, f(xi) ?x
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Figure 5.1.1, p. 289
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Figure 5.1.10, p. 292
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Example 2

• Find the area under the parabola y x2 from 0
  to 1.

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• ??????n?

• ???????,??x (b-a)/n

• ????????x??, xi a i ?x

n
n
Figure 5.1.7, p. 291
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• ???????????, f (xi) x2i

• ??????????, f (xi) ?x

• ?n????????

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