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Math Help - Antiderivative

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    Antiderivative

    Determine the antiderivative for f'(x)=\frac{1-20}{x^3}, f(1)=20
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    Quote Originally Posted by XIII13Thirteen View Post
    Determine the antiderivative for f'(x)=\frac{1-20}{x^3}, f(1)=20
    Are you sure? What's the point of the numerator?
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  3. #3
    Moo
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    Hello,

    Erm...
    Are you sure of 1-20 ?

    By the way, this is easy, because the antiderivative of \frac{1}{x^3}=x^{-3} is -\frac{1}{2} x^{-2} +C = \frac{-1}{2x^2} +C

    With C to be found with the indication f(1)=20
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  4. #4
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    Here is what you do

    Quote Originally Posted by XIII13Thirteen View Post
    Determine the antiderivative for f'(x)=\frac{1-20}{x^3}, f(1)=20
    you have \int{\frac{-19}{x^3}dx}=\frac{19}{2x^2}+Cand you know that f(1)=20...so \frac{19}{2(1)^2}+C=20...solve for C and you have your original function
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  5. #5
    Moo
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    It's \frac{-19}{x^3} ^^
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