1. The problem statement, all variables and given/known data For what values of K is the following integral improper? [tex]\int\stackrel{K}{0}x^2 / (x^2-19x+90) dx[/tex] 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.
An integral may be "improper" for one of several reasons- 1) The lower limit is [itex]-\infty[/itex]. 2) The upper limit is [itex]\infty[/itex]. 3) The integrand goes to [itex]-\infty[/itex] at some point in the interval of integration. 4) The integrand goes to [itex]\infty[/itex] 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?