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Math Help - A simple integral and a tricky volume problem

  1. #1
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    A simple integral and a tricky volume problem

    Coffee is draining from a full conical filter basket into a cylindrical coffee pot at the rate of 10in^3/min. How fast is the level in the pot rising when the height of the coffee in the filter is 5 inches? How fast is the level in the filter cone falling?

    6"
    ----------- -
    \ / |
    \ / |
    \------/<<<<<<< how fast does it fall?
    \ / 5"
    \ / |
    \ / |
    -

    ___________
    | |
    | |
    | |
    |-------------|<<<<<< How fast is this level rising?
    | |
    |__________|

    <---6"------->

    I am also stumped on another question which is probably easy for one of you the question is

    Evaluate

    the integral from -1 to 1 (sinx)/(1+x^2)dx <x in the denominator is being raised to the second power not everything sorry i do not know a better way of inputting this.

    I was wondering if someone may be able to solve this rather quickly, i have NO Clue what so ever to even begin doing this, this was an extra assignment that was given to us today and due tomorrow 7-28-09. Please answer asap, thank you very much for your help on the last problem and thank you in advance.


    P.S. i am sorry for posting in the wrong section, these questions come from my calc class.
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  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    the int from -a to a of an odd function is 0

    an odd function is one in which f(-x) = -f(x)

    sin(x)/(1+x^2) is odd since sin(-x)/[1+(-x)^2] = -sin(x)/(1+x^2)

    therefore the int is 0
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