Notices
Results 1 to 7 of 7

Thread: Help...please.

  1. #1 Help...please. 
    Forum Ph.D.
    Join Date
    Apr 2007
    Location
    "Jamerica"...When in America, Florida; when in Jamaica, St. Mary
    Posts
    959
    This came up on an AP Calc AB practice test; it's supposed to be easy to integrate, but I don't know how to:

    x^2(sqrt(x^3+1))

    Read: x squared times the square root of (x cubed plus one).

    Can anyone help? Don't just give the answer, please: give a fairly detailed explanation.

    Thanks,
    spt


    Whence comes this logic: no evidence = false?

    http://www.atheistthinktank.net/thinktank/index.php

    Theists welcome.
    ___________
    Reply With Quote  
     

  2.  

    Related Discussions:

     

  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
    Join Date
    Jul 2006
    Posts
    3,440
    Without actually trying it, it seems like integration by parts may be a good place to start. Edit: Or possibly using the substitution u=x^3, du=3x^2, I dunno. :P

    Edit again: Lance answered while I was making the above edit.


    Reply With Quote  
     

  4. #3  
    Forum Freshman
    Join Date
    May 2006
    Location
    maryland
    Posts
    18
    This problem is prime for a u substitution:

    u=x^3
    then,
    du=3*x^2*dx

    now substitute to get:

    (1/3)*sqrt(u+1)*du, if it is clear at this point what the integral will yield you can stop, but you can also do another substitution to make the answer more clear

    w=u+1
    dw=du

    so, now you have: (1/3)*sqrt(w)*dw

    integrate with respect to w and you get: (2/9)*w^(3/2)+C
    now substitute u back in: (2/9)*(u+1)^(3/2)+C
    now substitute x back in: (2/9)*(x^3+1)^(3/2)+C
    and that's the answer
    Reply With Quote  
     

  5. #4  
    Forum Ph.D.
    Join Date
    Apr 2007
    Location
    "Jamerica"...When in America, Florida; when in Jamaica, St. Mary
    Posts
    959
    MagiMaster,
    I'll see if I can do the integration by parts.

    Lance,
    I'm not familiar with the 'dw' thing...I guess it's not covered in Calc AB.

    Thanks!
    Whence comes this logic: no evidence = false?

    http://www.atheistthinktank.net/thinktank/index.php

    Theists welcome.
    ___________
    Reply With Quote  
     

  6. #5  
    Forum Radioactive Isotope MagiMaster's Avatar
    Join Date
    Jul 2006
    Posts
    3,440
    Well, substitution is much simpler than integration by parts. Gerenally speaking, integration by parts is a last resort unless you recognize certain patterns in the equations.
    Reply With Quote  
     

  7. #6  
    Forum Freshman
    Join Date
    May 2006
    Location
    maryland
    Posts
    18
    w is the same as u is the same as x. I could have chosen any variable, its just a substitution.In fact, if I had done the u substitution in this way:

    u=x^3+1

    I would not have had to do the w substituion. the only difference between the variables is the domain the integration lives on.

    for example if you were integrating the original function with respect to x from 2 to 4, then you would integrate the u substituted function with respect to u from 8 to 64. (because u=x^3 so 2^3 and 4^3).

    and then if you were integrating the w function with respect to w, you would integrate from 9 to 65. (because w=u+1 so 8+1 and 64+1).
    Reply With Quote  
     

  8. #7  
    Forum Freshman
    Join Date
    May 2007
    Posts
    30
    Nvm. just realised how old this topic is!
    Reply With Quote  
     

Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •