## Improper integral concept question

1. The problem statement, all variables and given/known data

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?
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 Quote by wetwilly92 1. The problem statement, all variables and given/known data 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.
 Recognitions: Gold Member Science Advisor Staff Emeritus 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?