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8.8 Improper Integrals

8.8 Improper Integrals. Math 6B Calculus II. Type 1: Infinite Integrals. Definition of an Improper Integral of Type 1 provided this limit exists (as a finite number). Type 1: Infinite Integrals. provided this limit exists (as a finite number). Type 1: Infinite Integrals.

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8.8 Improper Integrals

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  1. 8.8 Improper Integrals Math 6B Calculus II

  2. Type 1: Infinite Integrals • Definition of an Improper Integral of Type 1 provided this limit exists (as a finite number).

  3. Type 1: Infinite Integrals provided this limit exists (as a finite number).

  4. Type 1: Infinite Integrals • The improper integrals are called convergent if the corresponding limit exists and divergent if the limit does not exist.

  5. Type 1: Infinite Integrals

  6. The Integral of 1/xp

  7. Type 2: Discontinuous Integrals • Definition of an Improper Integral of Type 2 • If f is continuous on [a,b) and is discontinuous at b, then if this limit exists (as a finite number)

  8. Type 2: Discontinuous Integrals • b) If f is continuous on (a,b] and is discontinuous at a, then if this limit exists (as a finite number)

  9. Type 2: Discontinuous Integrals • The improper integral is called convergent if the corresponding limit exists and divergent if the limit does not exist.

  10. Type 2: Discontinuous Integrals • c) If f has a discontinuity at c, where a < c <b, and both are convergent, then we define

  11. A Comparison Test for Improper Integrals • Suppose that f and g are continuous functions with

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