# MAT136H1 Lecture Notes - Improper Integral

7.8 Integration Techniques

Improper Integrals

Question #1 (Easy): Improper Integrals With Infinite Interval

Strategy

There are two types of improper integrals: Type 1 is integrals with infinite interval, such as

,

, or

.

Type 2 is integrals whose interval is not infinite but fixed at , but has point(s) of discontinuity

within the interval, such as vertical asymptotes.

Sample Question

Explain why the given integral is improper.

Solution

The integral shows that the interval is . Since the interval is infinite, the integral is an improper

integral of Type 1.