improper integral

there are 2 types of Improper integrals
definition of an improper integral of type 1 – when the limits of integration are infinite
definition of an improper integral of type 2 – when the integrand becomes infinite within the interval of integration (like division by 0 for example)

so far we have dealt with integrals that gave us finite results for finite areas, here we deal with finite aswell as infinite integrals

improper integral type 1

improper integral of type 1 – when the limits of integration are infinite

consider the area below the function $\text{[math]}$ in the interval $\text{[math]}$ :

to calculate the area we use the integration method:
$\text{[math]}$

improper integral type 2

improper integral of type 2 – when the integrand becomes infinite within the interval of integration (like division by 0 for example

$\text{[math]}$ this function isnt defined at $\text{[math]}$ yet we integrate it which is why its called an improper integral
$\text{[math]}$

$\text{[math]}$ again this function isnt defined at $\text{[math]}$ but we integrate it anyway:
$\text{[math]}$

$\text{[math]}$