Results 1 to 13 of 13

Math Help - Integral - Pls check my work

  1. #1
    Super Member angel.white's Avatar
    Joined
    Oct 2007
    Posts
    723
    Awards
    1

    Integral - Pls check my work

    \int_{-1}^{1} (\sqrt[3]{u} + 1)^{2} du


    This is what I did:
    (FOIL)
    \int_{-1}^{1} ({u}^{2/3} + 2u^{1/3} + 1) du

    \left[ \frac{3}{5}u^{5/3} + \frac{3}{2}u^{4/3} + u + C\right]_{-1}^{1}

    \frac{3}{5}(1)^{5/3} + \frac{3}{2}(1)^{4/3} + 1 + C - \left(\frac{3}{5}(-1)^{5/3} + \frac{3}{2}(-1)^{4/3} - 1 + C \right)

    \frac{3}{5} + 1 + \frac{3}{5} + 1

    \frac{16}{5}

    But when I check it here: Function calculator it gives me what appears to be an imaginary number, it says the answer is: 4.53546396068 + 1.80971485451I_{3}. But I can't understand why, the negative ones should all work because they are never taken to an even root.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,906
    Thanks
    329
    Awards
    1
    Quote Originally Posted by angel.white View Post
    \int_{-1}^{1} (\sqrt[3]{u} + 1)^{2} du


    This is what I did:
    (FOIL)
    \int_{-1}^{1} ({u}^{2/3} + 2u^{1/3} + 1) du

    \left[ \frac{3}{5}u^{5/3} + \frac{3}{2}u^{4/3} + u + C\right]_{-1}^{1}

    \frac{3}{5}(1)^{5/3} + \frac{3}{2}(1)^{4/3} + 1 + C - \left(\frac{3}{5}(-1)^{5/3} + \frac{3}{2}(-1)^{4/3} - 1 + C \right)

    \frac{3}{5} + 1 + \frac{3}{5} + 1

    \frac{16}{5}

    But when I check it here: Function calculator it gives me what appears to be an imaginary number, it says the answer is: 4.53546396068 + 1.80971485451I_{3}. But I can't understand why, the negative ones should all work because they are never taken to an even root.
    Funny. It told me that (u^{1/3} + 1)^2 didn't exist on the whole interval.

    I guess the solution is that Function calculator sucks.

    I got your answer.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by topsquark View Post
    Funny. It told me that (u^{1/3} + 1)^2 didn't exist on the whole interval.

    I guess the solution is that Function calculator sucks.

    I got your answer.

    -Dan
    did you try evaluating the second part of his answer in a regular calculator?

    maple gave me a complex answer as well, i can't see why at the moment
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,906
    Thanks
    329
    Awards
    1
    Quote Originally Posted by Jhevon View Post
    did you try evaluating the second part of his answer in a regular calculator?

    maple gave me a complex answer as well, i can't see why at the moment
    I looked at his solution (and found no errors) and after seeing how bad the function calculator was, I ran it through my TI-92.

    My guess is that the programs are having trouble with the cube root for negative x. (Though you would think that Maple at least wouldn't have that problem.)

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by topsquark View Post
    I looked at his solution (and found no errors) and after seeing how bad the function calculator was, I ran it through my TI-92.

    My guess is that the programs are having trouble with the cube root for negative x. (Though you would think that Maple at least wouldn't have that problem.)

    -Dan
    which brings up another interesting--maybe related--point. when you try to graph x^(1/3) with Graph, it only graphs the function for positive x's. why is it that programs have trouble evaluating the odd roots of negative numbers? is it a glich, or do they know something that we don't?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    Mine works perfectly fine for negative x
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member angel.white's Avatar
    Joined
    Oct 2007
    Posts
    723
    Awards
    1
    Quote Originally Posted by DivideBy0 View Post
    Mine works perfectly fine for negative x
    Which do you use? & is it free?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by angel.white View Post
    Which do you use? & is it free?
    Graph is free, and it works great (except, perhaps, in this situation ). do you have it?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member angel.white's Avatar
    Joined
    Oct 2007
    Posts
    723
    Awards
    1
    Quote Originally Posted by Jhevon View Post
    Graph is free, and it works great (except, perhaps, in this situation ). do you have it?
    No, I just downloaded it, I'll give it a try.

    I've been using:
    Cool math .com - Online Graphing Calculator - Graph It!
    and Function Grapher Online
    Follow Math Help Forum on Facebook and Google+

  10. #10
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by angel.white View Post
    No, I just downloaded it, I'll give it a try.

    I've been using:
    Cool math .com - Online Graphing Calculator - Graph It!
    and Function Grapher Online
    well, Graph does a lot more than just plot graphs. it does other cool things, like finding the area under curves and stuff
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Super Member angel.white's Avatar
    Joined
    Oct 2007
    Posts
    723
    Awards
    1
    Quote Originally Posted by Jhevon View Post
    Graph is free, and it works great (except, perhaps, in this situation ). do you have it?
    Wow, it's a pretty neat program I like how easy it is to check an answer, click the shady parabola thing :P

    But, it also could not verify the answer for negative numbers, said it was imaginary. But I checked my answer anyway by taking it from 0 to 1 instead, and graph agreed with me, so if I got it wrong, then it's only due to an arithmetic error at the end. And that is rather unlikely as topsquark got the same answer.

    On a side note, I wish I was a robot.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Super Member angel.white's Avatar
    Joined
    Oct 2007
    Posts
    723
    Awards
    1
    Quote Originally Posted by Jhevon View Post
    well, Graph does a lot more than just plot graphs. it does other cool things, like finding the area under curves and stuff
    And make smiley faces.
    Attached Thumbnails Attached Thumbnails Integral - Pls check my work-smiley-face.jpg  
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,906
    Thanks
    329
    Awards
    1
    (Someone has a lot of spare time on their hands!)

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 1st 2011, 06:49 PM
  2. Replies: 4
    Last Post: March 12th 2011, 04:05 AM
  3. Can someone check my integral work?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 20th 2010, 10:00 AM
  4. Replies: 3
    Last Post: April 10th 2009, 10:38 PM
  5. Please Check My Work: Integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 28th 2007, 02:26 PM

Search Tags


/mathhelpforum @mathhelpforum