Section 43 Riemann Sums and Definite Integrals
Section43and44.notebook
May 22, 2012
Section 43 Riemann Sums and Definite Integrals Definition of a Definite Integral If f is defined on the closed interval [a,b] and the limit
exists, then f is integrable on [a,b] and the limit is
Nov 289:17 AM
Theorem 44:
If a function f is continuous on the closed interval [a,b], then f is integrable on [a,b].
Nov 289:22 AM
1
Section43and44.notebook
May 22, 2012
Theorem 45: The Definite Integral as the Area of a Region. If f is continuous and nonnegative on the closed interval [a,b], then the area of the region bounded by the graph of f, the xaxis and the vertical lines x=a and x=b is given by:
Nov 289:24 AM
Special Integrals
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2
Section43and44.notebook
May 22, 2012
Theorem 46: Additive Interval Property
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Theorem 47 Properties of Definite Integrals
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3
Section43and44.notebook
May 22, 2012
Theorem 48
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Examples: Page 278 9) Write the limit as a definite integral on the interval [a,b], where is any point in the ith subinterval.
Nov 289:34 AM
4
Section43and44.notebook
May 22, 2012
23) Sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral.
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5
Section43and44.notebook
May 22, 2012
Nov 289:55 AM
Evaluate the Integral using the following values
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6
Section43and44.notebook
May 22, 2012
Nov 2810:00 AM
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7
Section43and44.notebook
May 22, 2012
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Section43and44.notebook
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Section43and44.notebook
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MORE EXAMPLES (Section 44) Page 291
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Section43and44.notebook
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Section43and44.notebook
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25)
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Section43and44.notebook
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TEST Friday Sections 41,42,43 and 44. Optional Review Problems Page 255#2331odd,3541odd Page 291#27,29 Page279#2735odd Page291#1731odd Nov 299:44 AM
13
May 22, 2012
Section 43 Riemann Sums and Definite Integrals Definition of a Definite Integral If f is defined on the closed interval [a,b] and the limit
exists, then f is integrable on [a,b] and the limit is
Nov 289:17 AM
Theorem 44:
If a function f is continuous on the closed interval [a,b], then f is integrable on [a,b].
Nov 289:22 AM
1
Section43and44.notebook
May 22, 2012
Theorem 45: The Definite Integral as the Area of a Region. If f is continuous and nonnegative on the closed interval [a,b], then the area of the region bounded by the graph of f, the xaxis and the vertical lines x=a and x=b is given by:
Nov 289:24 AM
Special Integrals
Nov 289:26 AM
2
Section43and44.notebook
May 22, 2012
Theorem 46: Additive Interval Property
Nov 289:28 AM
Theorem 47 Properties of Definite Integrals
Nov 289:29 AM
3
Section43and44.notebook
May 22, 2012
Theorem 48
Nov 289:31 AM
Examples: Page 278 9) Write the limit as a definite integral on the interval [a,b], where is any point in the ith subinterval.
Nov 289:34 AM
4
Section43and44.notebook
May 22, 2012
23) Sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral.
Nov 289:46 AM
Nov 289:49 AM
5
Section43and44.notebook
May 22, 2012
Nov 289:55 AM
Evaluate the Integral using the following values
Nov 289:57 AM
6
Section43and44.notebook
May 22, 2012
Nov 2810:00 AM
Nov 281:56 PM
7
Section43and44.notebook
May 22, 2012
Nov 281:59 PM
Nov 282:02 PM
8
Section43and44.notebook
May 22, 2012
Nov 282:04 PM
Nov 282:06 PM
9
Section43and44.notebook
May 22, 2012
Nov 282:09 PM
MORE EXAMPLES (Section 44) Page 291
Nov 298:56 AM
10
Section43and44.notebook
May 22, 2012
Nov 299:00 AM
Nov 299:02 AM
11
Section43and44.notebook
May 22, 2012
Nov 299:04 AM
25)
Nov 299:06 AM
12
Section43and44.notebook
May 22, 2012
Nov 282:12 PM
TEST Friday Sections 41,42,43 and 44. Optional Review Problems Page 255#2331odd,3541odd Page 291#27,29 Page279#2735odd Page291#1731odd Nov 299:44 AM
13
