Improper integral concept question

[wetwilly92]

Homework Statement

For what values of K is the following integral improper?

$$\int\stackrel{K}{0}x^2 / (x^2-19x+90) dx$$I'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?

$$\int\stackrel{K}{0}x^2 / (x^2-19x+90) dx$$I'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?