Results 1 to 9 of 9

Math Help - Substituting numbers into an integral.

  1. #1
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
    From
    The raggedy edge.
    Posts
    782

    Substituting numbers into an integral.



    My problem is that I can't seem to substitute numbers into an integral properly !

    One of my concerns is that my evaluation of I0 is different if I use the integral or use the expression (-sinh1 and sinh1 respectively). Since the expression is correct, as it was a "prove that" question and therefore written in the book, i'm not really sure why i'm getting two different answers.

    I can't see any problem with my working for part (b). That's just one of the reasons why this is so infuriating!

    Anyway, if anyone could see what i'm doing wrong it would be a great help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
    From
    The raggedy edge.
    Posts
    782
    I managed to find another question that I can't do with the same problem: I can't substitute numbers into an expression!

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hi,

    For the first problem, question a), I don't see why you say it's wrong... ?

    Now, for question b), I know there's a problem :

    \int_1^0 x \cosh(x) ~dx=[x \sinh(x)]_1^0-\int_1^0 \sinh(x) ~dx

    But [x \sinh(x)]_1^0=[f(x)]_1^0=f(0)-f(1)={\color{red}-} \sinh(1)

    And \int_1^0 \sinh(x) ~dx=\cosh(0)-\cosh(1)=1-\cosh(1)

    \implies I_1={\color{red}-} \sinh(1)+\cosh(1)-1


    Now, there's a possibility that your answers have been given in a form with exponentials.

    Just use :
    \cosh(x)=\frac{e^x+e^{-x}}{2} and \sinh(x)=\frac{e^x-e^{-x}}{2}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by Showcase_22 View Post
    I managed to find another question that I can't do with the same problem: I can't substitute numbers into an expression!

    It's normal

    I_{5,6}=\frac{5!6!}{11!} \cdot {\color{red}I_{0,11}}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
    From
    The raggedy edge.
    Posts
    782
    For part a) my book gives the answer as 37sinh1-28cosh1. They've got this answer by making I0=sinh1 instead of -sinh1. I just thought I needed a second opinion before I branded the book incorrect.

    For the second question they get:



    I couldn't see where my answer was going wrong because it looks so straightforward!

    Thanks for pointing out my mistake for the second question. The boundaries for the integral are the other way around from what i'm used to.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by Showcase_22 View Post
    For part a) my book gives the answer as 37sinh1-28cosh1. They've got this answer by making I0=sinh1 instead of -sinh1. I just thought I needed a second opinion before I branded the book incorrect.
    Well, I've check several times... all getting -sinh(1)
    I don't see where the mistake would be

    For the second question they get:



    I couldn't see where my answer was going wrong because it looks so straightforward!
    Yes, if you calculate I_(0,11), you'll get a factor 2^(12)

    Thanks for pointing out my mistake for the second question. The boundaries for the integral are the other way around from what i'm used to.
    Ya I know... If it really disturbs you, you can work on \int_0^1 \dots ~dx=-\int_1^0 \dots ~dx

    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
    From
    The raggedy edge.
    Posts
    782
    hmmm.

    The general consensus is that a) is right but incorrect in the book and b) was incorrectly done by me (whoops!).

    I finally get their answer for the second question! I didn't include I_(0,11) because I thought it was 0 since I used the expression (darn!!). Anyhow, it's great that I finally understand what i'm doing!

    Follow Math Help Forum on Facebook and Google+

  8. #8
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by Showcase_22 View Post
    hmmm.

    The general consensus is that a) is right but incorrect in the book and b) was incorrectly done by me (whoops!).
    Okay, I've figured out the problem...

    The formula is :

    \boxed{I_n={\color{red}-\sinh(1)+n \cosh(1)}+n(n-1) I_{n-2}}

    I thought the formula was ok because it was the book's ^^'

    I finally get their answer for the second question! I didn't include I_(0,11) because I thought it was 0 since I used the expression (darn!!). Anyhow, it's great that I finally understand what i'm doing!

    Yep, that was the missing step ^^ I thought you already knew when you last posted !
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
    From
    The raggedy edge.
    Posts
    782
    lol, I know i'm a little slow. In my weak (but flimsy!) defence I was stuck on some other questions as well.

    Since I now regard this place as the fountain of all mathematical knowledge, I might post them since i've just about reached the end of my tether!!

    Thanks for your help! You're pretty darn good at this maths malarkey!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Substituting equation
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: April 29th 2011, 12:00 AM
  2. Help substituting !
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: April 17th 2010, 06:24 PM
  3. Substituting
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: October 6th 2009, 03:29 PM
  4. Substituting f(x)
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 3rd 2009, 06:38 AM
  5. Integral. Substituting makes it more complex
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 3rd 2007, 05:45 PM

Search Tags


/mathhelpforum @mathhelpforum