Improper_Integrals.ppt

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IMPROPER INTEGRALS
Improper Integral
TYPE-II Discontinuous Integrand Integrands with
Vertical Asymptotes
TYPE-I Infinite Limits of Integration
Example
Example
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IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1
Example
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IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1
Example
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IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1
The improper integrals are called convergent
if the corresponding limit exists and divergent
if the limit does not exist.
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IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1
Example
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IMPROPER INTEGRALS
082
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IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1
convergent
If both improper integrals are convergent
Example
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IMPROPER INTEGRALS
Memorize
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IMPROPER INTEGRALS
Improper Integral
TYPE-II Discontinuous Integrand Integrands with
Vertical Asymptotes
TYPE-I Infinite Limits of Integration
Example
Example
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IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2
Example
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IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2
Example
Example
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IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2
Example
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IMPROPER INTEGRALS
F092
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IMPROPER INTEGRALS
Example
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IMPROPER INTEGRALS
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IMPROPER INTEGRALS
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IMPROPER INTEGRALS
F112
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IMPROPER INTEGRALS
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IMPROPER INTEGRALS
F092
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IMPROPER INTEGRALS
F102
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