Improper integrals

  • Thread starter aaaa202
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  • #1
1,170
3

Homework Statement


Check if the following integrals diverge:
Int(1/(x^3-2x^2+x), from 0 to 1) and Int(1/(x^3+x^2-2x)

Homework Equations


Ratio-test(not sure if thats the name)


The Attempt at a Solution


I have solved the problem and found that both integrals diverge at x=0. I just want to check if you guys agree with me.
 

Answers and Replies

  • #2
Ratio test is for infinite series, not a improper integrals. It would be helpful to see your work.
 
  • #3
35,057
6,793

Homework Statement


Check if the following integrals diverge:
Int(1/(x^3-2x^2+x), from 0 to 1) and Int(1/(x^3+x^2-2x)

Homework Equations


Ratio-test(not sure if thats the name)


The Attempt at a Solution


I have solved the problem and found that both integrals diverge at x=0.
Both integrands are undefined at x = 0, which is why the integrals are improper. Both integrands are also undefined at the other endpoint, x = 1.

You need to use limits to evaluate these integrals - then you can decide whether either one diverges.
I just want to check if you guys agree with me.
 
  • #4
1,170
3
Okay ratio test was then not the correct name. What I did was use the test that if limx->0[g/f>0] then g also diverges if f diverges. So I took f as 1/x^3. Isn't this correct, and dont you guys get that both integrals diverge?
 

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