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Improper integral concept question 
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#1
Mar3011, 01:00 AM

P: 8

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^219x+90) dx[/tex] I'm stuck on this question. I understand mechanically, that the integration require partial fraction decomp, which results in 9ln(x9) (from 0 to K) + 10ln(x10) (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? 


#2
Mar3011, 03:59 AM

P: 146

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


#3
Mar3011, 06:31 AM

Math
Emeritus
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Thanks
PF Gold
P: 39,510

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? 


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