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: Simply Checking an Answer in Calculus

  1. Feb 27, 2005 #1
    Hello all, again.

    Simple question.

    Compute [tex]\int_{9}^{4} (x - \frac{1}{\sqrt{x}}) dx[/tex]

    I did this:

    [tex]\int_{9}^{4} (x - \frac{1}{x^{0.5}}) dx[/tex] = [tex]\int_{9}^{4} (x - x^{-0.5}) dx[/tex]

    [tex]\left[ \frac{1}{2} x^2 - 2 x^{0.5} \right]_{9}^{4}[/tex] = [tex]\left[ \frac{x^2}{2} - 2 \sqrt{x} \right]_{9}^{4}[/tex]

    [tex](\frac{81}{2} - 6) - (\frac{16}{2} - 4) = \frac{81 - 12}{2} - \frac{16 - 8}{2} = \frac{69}{2} - \frac{8}{2} = \frac{61}{2} = 30.5[/tex]

    2 months of calculus and and still I am not sure of what I have done wrong. The answers in my book gives [tex]10 \frac{2}{3}[/tex]

    So if it is right then can someone enlighten me to what I have done wrong please.


    The Bob (2004 ©)
  2. jcsd
  3. Feb 27, 2005 #2
    Third step...
    x - x^-0.5 gives 1/2x^2 - 2x^0.5... hmmm...
    Your work looks right to me.. maybe a book error?
    Last edited: Feb 27, 2005
  4. Feb 27, 2005 #3
    That is what I was hoping for. I know I make simply mistakes but now 4 people reckon it is right.

    Cheers. Still though, can anyone else see anything wrong at all???

    The Bob (2004 ©)
  5. Feb 27, 2005 #4


    User Avatar
    Science Advisor
    Homework Helper

    Nope,both your and the books answers are incorrect.My answer is [tex] -\frac{61}{2} [/tex] and i'm sure of it,because even my old rusty Maple says it is so...:wink:

  6. Feb 27, 2005 #5
    That's just weird.. even my calculator gives 30.5. :\
    And yeah, I get the negative answer too... only mistake in his work I see now.
  7. Feb 27, 2005 #6
    Oh nuts. I see what I did wrong. I have written the original limtis of the question the wrong way around. My fault (obviously). I'm not used to the Tex of calculus problems.

    It should have been [tex]\int_{4}^{9} (x - \frac{1}{\sqrt{x}}) dx[/tex] to give [tex]\frac{61}{2}[/tex]

    Cheers. At least I can go to college on Wednesday and now I am right. :biggrin:

    The Bob (2004 ©)
  8. Feb 27, 2005 #7


    User Avatar
    Science Advisor
    Homework Helper

    It seemed pretty weird to me too,with the larger value being the inferior limit,but,hey,anything is possible in mathemetics,right...?:wink:

  9. Feb 28, 2005 #8
    Most things are possible but I am yet to see a larger, inferior limit too, Daiel. :wink:

    The Bob (2004 ©)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook