1. This site uses cookies. By continuing to use this site, you are agreeing to our use of cookies. Learn More.

Homework Assistance

Discussion in 'Chit Chat' started by vyvance, Feb 20, 2012.

  1. vyvance

    Full Member

    Joined:
    Nov 6, 2011
    Messages:
    605
    Likes Received:
    0
    Location:
    Texas
    Doing my review for the calculus test later this week, and I've reached a problem I'm having trouble with. Any help would be appreciated.

    Key:
    fnInt = intergral
    sqrt = square root
    abs = absolute value


    Evaluate the integral.

    fnInt[ dx / ( x sqrt((9x^2) - 7))

    I'm solving using u substitution.
    u = 3x
    du = 3dx
    1/3 du = dx

    The review says the answer is:
    (sqrt(7) / 21) (sec^-1) abs( (3/7) sqrt(7) x) + C

    I keep getting the following for my answer:
    (sqrt(7) / 7) (sec^-1) abs( (3/7) sqrt(7) x) + C

    I'm not sure where it is getting that 21 from at the bottom of the first fraction. I've tried multiple times now, but I just can't figure it out.

    Thanks in advance if anyone can assist me.
     
  2. Fiddledeedee

    Full Member

    Joined:
    May 10, 2011
    Messages:
    955
    Likes Received:
    0
    Location:
    England
    [Note: fiddledeedee's mathsy sibling speaking (with permission)]

    I haven't stepped through the entire integral, but at a guess, could you have missed a divide-by-3 -- the substitution gives dx -> du/3 on the top and x -> u/3 on the bottom (since u = 3x). Before applying a standard integral, I get to: Integral(1 / (u sqrt(u^2 - 7)), du), but I don't really have time to do the standard integral or parts tonight.
     
  3. alex1170

    Full Member

    Joined:
    Dec 14, 2011
    Messages:
    400
    Likes Received:
    1
    Location:
    California
    #3 alex1170, Feb 20, 2012
    Last edited: Feb 20, 2012
  4. Zontar

    Full Member

    Joined:
    Oct 22, 2010
    Messages:
    1,802
    Likes Received:
    0
    Location:
    Binghampton, NY
    This, of course, best used when attempting the problem first.

    Believe me, you'll fail out pretty quickly if you use computers to do all your homework. Use it for the part you're stuck on and try to take it yourself from there.
     
  5. FJ Cruiser

    Full Member

    Joined:
    Jul 17, 2011
    Messages:
    1,004
    Likes Received:
    0
    Location:
    Deep in the Heart
    My first instinct is to say that you're forgetting to multiply that function by the 1/3 you pulled outside the integral when you did your substitution. I would try to work on it more, but I have my own calculus and physics I need to do. :/
     
  6. vyvance

    Full Member

    Joined:
    Nov 6, 2011
    Messages:
    605
    Likes Received:
    0
    Location:
    Texas
    Thanks for the responses. I'll look it over some more with that in mind.