1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Converge or diverge

  1. Mar 24, 2014 #1
    1. The problem statement, all variables and given/known data
    ∫from 1 to 8 of (-1/(x-3)^2 dx
    Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it diverges to infinity, state your answer as INF. If it diverges to negative infinity, state your answer as MINF. If it diverges without being infinity or negative infinity, state your answer as DIV.

    ANS: DIVERGES TO -INFINITY

    MY PROBLEM: I KEEP GETTING THAT IT DIVERGES TO +INFINITY

    3. The attempt at a solution

    solved for antiderv and got 1/(x-3)
    so lim c--> c- [(1/(x-3)) from 1 to c]+ c--> c+ (1/(x-3))from c to 8.
    Working this out, I get
    infinity - 3/10 + infinity.
    How is the answer diverge to -infinity?
     
  2. jcsd
  3. Mar 24, 2014 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    I think what you actually meant was the integral becomes
    $$\lim_{c \to 3^-} \left.\frac{1}{x-3}\right|_1^c + \lim_{c \to 3^+} \left. \frac{1}{x-3}\right|_c^8.$$ Please show us how you evaluated this to get ##+\infty##.
     
  4. Mar 24, 2014 #3
    [1/c-3 approaching from the left gives infinity + 1/2] + [1/5 - 1/c-3 from the positive side is -infinity]
    so I get infinity + (-infinity) = infinity
    I know I did something wrong there. I just don't know what.
     
  5. Mar 24, 2014 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Check the sign of the first infinity.
     
  6. Mar 24, 2014 #5
    isn't it positive? when i graphed it, that graph approaching from the left went straight up
     
  7. Mar 24, 2014 #6

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Not if you graphed 1/(x-3). What's the sign of x-3 when you approach from the left?
     
  8. Mar 26, 2014 #7
    Ohh I see what you mean. I was not distributing my negative after I took the antiderivative and I was graphing -1/(x-3). Thank you very much.
    So it would be (-inf + 1/2) + (-1/5 -infinity)= -infinity.
     
  9. Mar 26, 2014 #8

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Right!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Converge or diverge
  1. Converge or Diverge? (Replies: 5)

  2. Divergent or Convergent? (Replies: 17)

Loading...