calc

how would you do this improper integral

1/(x-1)
from 0 to 2

this is improper at one, so I split it up into two integrals
ln(x-1) from 0-1 and
ln(x-1) from 1-2

I then did for the first one the (lim t->1(-) of ln(t-1))-(ln(0-1))

and then the same thing for the second part
I didn't know if this was right though, or what the answer would be

  1. 👍
  2. 👎
  3. 👁
  1. You need to include absolute value signs in the argument of the logarithm:

    ln|x-1| from 0-1 and
    ln|x-1| from 1-2

    What you find is that both the limits diverge logarithmically, so the integral doesn't exist. However, if you add both the terms together and take the limit in one go, then the divergent terms cancel. This is called the Cauchy principal value of the integral.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Chemistry

    What is the complete ionic equation for NaOH(aq) + Fe(NO3)3(aq)? I'm putting this on webassign, but it's telling me "One or more of your reactants appear to have an improper oxidation state. One or more of your products contains

  2. math

    Express 4 8/9 as an improper fraction A. 36/9 B. 21/9 C.44/9 D. 40/9 B?

  3. math

    write each mixed number as an improper fraction 1 7/8

  4. Calculus

    Which of the following is an improper integral? a) integral from 0 to 3 of (x+1)/(3x-2) dx b) integral from 1 to 3 of (x+1)/(3x-2) dx c) integral from -1 to 0 of (x+1)/(3x-2) dx d) None of these Please help I don't know which one?

  1. Business Math

    Convert the following mixed number to an improper fraction: 12 3/4

  2. math

    write 5 3/10 as an improper fraction a. 53/10 b. 25/10 c. 47/10 d. 50/10

  3. 11th grade

    what is the 10 and 5 \12 as equilvalent improper fraction

  4. math

    Write 7 3/5 as an improper fraction

  1. math

    how do i change 9 5/9 to an improper fraction

  2. Math

    Write 3 1/3 as an improper fraction.

  3. Math

    Write 2 1/2 as an improper fraction.

  4. Algebra

    a student's work to solve 2 6/7 divided by 2/7 is shown below. which of the following statements do you agree with? 2 6/7 divided by 2/7 = 19/7 divided by 2/7= 7/19 times 2/7= 7/19 times 2/7=2/19 cross out the 7 in the first one

You can view more similar questions or ask a new question.