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!

Homework Help: Evaluate the Improper integral [4,13] 1/(x-5)^(1/3)

  1. Apr 12, 2015 #1
    1. The problem statement, all variables and given/known data

    Evaluate the Improper integral [4,13] 1/(x-5)1/3

    2. Relevant equations


    3. The attempt at a solution
    In step 1, I split the integral into two separate integrals because at x=5, it would be undefined. I made the first limit approach 5 from the left and the second limit approach five from the right.

    For step 2, I did u substitution to prepare to integrate. Since I did the substitution, I plugged the old intervals into u = x - 5 to get the new ones.

    For step 3, I rewrote both integrals in terms of u du and brought the u^(1/3) from the denominator to the numerator for easier integration. I also added the new intervals in.

    In step 4, I integrated both integrals.

    Step 5 is where I'm not sure what to do. I plugged in the values and that is what I ended up with but in the first parentheses, the second value has a (-1)2/3 which is undefined. The (R-5)'s will equal 0 and cancel those fractions out but I don't know how to handle the (-1)2/3.
  2. jcsd
  3. Apr 12, 2015 #2


    Staff: Mentor

    ##(-1)^{2/3}## is defined -- its value is 1.

    You can work with it either as ##[(-1)^2]^{1/3} = 1^{1/3} = 1## or as ##[(-1)^{1/3}]^2 = (-1)^2 = 1##.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted