   Chapter 7.R, Problem 7CC

Chapter
Section
Textbook Problem

# Define the improper integral ∫ a b f ( x )   d x for each of the following cases.(a) f has an infinite discontinuity at a.(b) f has an infinite discontinuity at b.(c) f has an infinite discontinuity at c, where a < c < b .

To determine

To Define: The integral abf(x)dx, when it has infinite discontinuity.

Explanation

The improper integrals are defined as the limit of proper integral(s).

(a)

The integral abf(x)dx, when it has infinite discontinuity at a, is defined as the limit of the proper integral λbf(x)dx.

abf(x)dx=limλa+λbf(x)dx

Provided this limit exists

(b)

The integral abf(x)dx, when it has infinite discontinuity at b, is defined as the limit of the proper integral aλf(x)dx

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