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Help with integration question

  • 03-05-2010 01:52PM
    #1
    Heffo91
    Closed Accounts Posts: 12 ✭


    hey im trying to redo my mock deb paper 1 i think! im stuck on how to integrate the following problem: 1/*sqrt 8-x^2
    it was b)ii) on Q8.
    any help would be appreciated


Comments

  • #2
    **Timbuk2**
    Moderators, Education Moderators, Motoring & Transport Moderators Posts: 7,396 Mod ✭✭✭✭**Timbuk2**


    Do you mean it looks like this?
    [latex]\displaystyle \int_0^1{\frac{1}{8 - x^2}}\,dx[/latex]

    In that case, isn't that just one of those ones where you go to the tables (I don't have them handy, so I'm not sure if it is)?

    Possibly, you would do something like this. Factor out a minus from the bottom, to get
    [latex]\displaystyle -\int_0^1{\frac{1}{x^2 - 8}}\,dx[/latex]

    and rewrite as

    [latex]\displaystyle -\int_0^1{\frac{1}{x^2 - (\sqrt{8})^2}}\,dx[/latex]

    Go to your tables, and there should be some standard integral that looks like that.


  • #3
    **Timbuk2**
    Moderators, Education Moderators, Motoring & Transport Moderators Posts: 7,396 Mod ✭✭✭✭**Timbuk2**


    Actually, there is no need to factor out the minus, there is a formula in the tables that looks like this:

    [latex]\displaystyle \int{\frac{1}{a^2 - x^2}} = \frac{1}{2a}\ln|\frac{a+x}{a-x}|[/latex]


  • #4
    MathsManiac
    Registered Users, Registered Users 2 Posts: 1,595 ✭✭✭MathsManiac


    I suspect, (for no obvious reason,) that the OP might have meant
    [latex]\displaystyle \int{\frac{1}{\sqrt{8 - x^2}}} [/latex]

    If so, there's another formula in the tables that does the trick, giving
    [latex]\displaystyle \sin^{-1}{\frac{x}{\sqrt{8}}} [/latex]


  • #5
    **Timbuk2**
    Moderators, Education Moderators, Motoring & Transport Moderators Posts: 7,396 Mod ✭✭✭✭**Timbuk2**


    MathsManiac wrote: »
    I suspect, (for no obvious reason,) that the OP might have meant
    [latex]\displaystyle \int{\frac{1}{\sqrt{8 - x^2}}} [/latex]

    If so, there's another formula in the tables that does the trick, giving
    [latex]\displaystyle \sin^{-1}{\frac{x}{\sqrt{8}}} [/latex]

    Ah yea, I missed that!

    Sorry for the confusion :o


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