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Math Help - Anti derivative

  1. #1
    Junior Member
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    Mar 2007
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    43

    Anti derivative

    Hello,

    Here is the problem

    Consider the function .
    Let be the antiderivative of with .
    Then ______


    I get this far...

    (x^6)/6+ (5x^2)/4


    or is it

    (x^6)/6=(15/2)x^(3/2)
    what's next?
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  2. #2
    Senior Member
    Joined
    Apr 2006
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    401
    Quote Originally Posted by xcelxp View Post
    Hello,

    Here is the problem

    Consider the function .
    Let be the antiderivative of with .
    Then ______


    I get this far...

    (x^6)/6+ (5x^2)/4


    what's next?
    How in the world did you try integrate that?

    If f(x) = x^5 + 5*sqrt(x) = x^5 + 5*x^(1/2), then

    F(x) = (x^6)/6 + (5*x^(3/2))/(3/2) = (x^6)/6 + (10x^(3/2))/3 + C

    We are given F(1) = -4; thus,

    -4 = 7/2 + C (we got this by plugging 1 in for all the x's above)

    Solve for C:

    C = -15/2.

    Replace the C above with what you solved, and you have F(x).
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  3. #3
    Junior Member
    Joined
    Mar 2007
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    first one was with a calculator... 2nd was me.. lol .. thanks!
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