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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 on theme: "Example IMPROPER INTEGRALS Improper Integral TYPE-I: Infinite Limits of Integration TYPE-I: Infinite Limits of Integration Example TYPE-II: Discontinuous."— Presentation transcript:

1 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

2 IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1 Example

3 IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1 Example

4 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.

5 IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1 Example

6 IMPROPER INTEGRALS 082

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

8 Memorize: IMPROPER INTEGRALS

9 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

10 IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2 Example

11 IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2 Example

12 IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2 Example

13 IMPROPER INTEGRALS F092

14 IMPROPER INTEGRALS Example

15 IMPROPER INTEGRALS

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17 F112

18 IMPROPER INTEGRALS

19 F092

20 IMPROPER INTEGRALS F102

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