Improper integral concept question


by wetwilly92
Tags: concept, improper, integral
wetwilly92
wetwilly92 is offline
#1
Mar30-11, 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^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?
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Tangent87
Tangent87 is offline
#2
Mar30-11, 03:59 AM
P: 146
Quote Quote by wetwilly92 View Post
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.
HallsofIvy
HallsofIvy is online now
#3
Mar30-11, 06:31 AM
Math
Emeritus
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PF Gold
P: 38,890
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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