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  The improper integrals are called convergent if the corresponding limit exists and divergent if the limit does not exist.

Type 1: Infinite Integrals

The Integral of 1/x p

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)

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)

Type 2: Discontinuous Integrals

 c) If f has a discontinuity at c, where a < c <b, and both are convergent, then we define

A Comparison Test for Improper Integrals  Suppose that f and g are continuous functions with