Example IMPROPER INTEGRALS Improper Integral TYPE-I: Infinite Limits of Integration TYPE-I: Infinite Limits of Integration Example TYPE-II: Discontinuous.

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Presentation transcript:

Example IMPROPER INTEGRALS Improper Integral TYPE-I: Infinite Limits of Integration TYPE-I: Infinite Limits of Integration Example TYPE-II: Discontinuous Integrand Integrands with Vertical Asymptotes TYPE-II: Discontinuous Integrand Integrands with Vertical Asymptotes

IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1 Example

IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1 Example

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.

IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1 Example

IMPROPER INTEGRALS 082

IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1 If both improper integrals are convergent convergent Example

Memorize: IMPROPER INTEGRALS

Example IMPROPER INTEGRALS Improper Integral TYPE-I: Infinite Limits of Integration TYPE-I: Infinite Limits of Integration Example TYPE-II: Discontinuous Integrand Integrands with Vertical Asymptotes TYPE-II: Discontinuous Integrand Integrands with Vertical Asymptotes

IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2 Example

IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2 Example

IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2 Example

IMPROPER INTEGRALS F092

IMPROPER INTEGRALS Example

IMPROPER INTEGRALS

F112

IMPROPER INTEGRALS

F092

IMPROPER INTEGRALS F102

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