Improper integral concept question

[wetwilly92]

Homework Statement

For what values of K is the following integral improper?

\int\stackrel{K}{0}x^2 / (x^2-19x+90) dxI'm stuck on this question. I understand mechanically, that the integration require partial fraction decomp, which results in -9ln(x-9) (from 0 to K) + 10ln(x-10) (from 0 to K). What I don't understand is what makes this integral improper. I understand that LN is undefined for all evaluations < 1. So does this mean that any K < 10 will create an improper integral?

EDIT: How does one properly display the upper and lower limits on the integration symbol?

 

[Tangent87]

Homework Statement

For what values of K is the following integral improper?

\int\stackrel{K}{0}x^2 / (x^2-19x+90) dxI'm stuck on this question. I understand mechanically, that the integration require partial fraction decomp, which results in -9ln(x-9) (from 0 to K) + 10ln(x-10) (from 0 to K). What I don't understand is what makes this integral improper. I understand that LN is undefined for all evaluations < 1. So does this mean that any K < 10 will create an improper integral?

EDIT: How does one properly display the upper and lower limits on the integration symbol?

To get the limits right use \int_0^K instead of stackrel.

As for the question itself, you might want to draw a sketch of the function.

 

[HallsofIvy]

An integral may be "improper" for one of several reasons-
1) The lower limit is -\infty.
2) The upper limit is \infty.
3) The integrand goes to -\infty at some point in the interval of integration.
4) The integrand goes to \infty at some point in the interval of integration.

Which of those can happen here?

What values of x make the denominator of the integrand 0?