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Calculus

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Consider the function f(x)=(7/x^2)-(6/x^6).
Let F(x) be the antiderivative of f(x) with F(1)=0.
Then F(2) equals _____.

  • Calculus - ,

    Write it as
    f(x) = 7x^-2 - 6x^-6
    F(x)= -7x^-1 + (6/5)x^-5 + c

    F(2) = -7/2 + (6/5)/2^5 + c
    = ......

  • Calculus - ,

    since F(1) = 0, we have
    -7 + 6/5 + c = 0

    which you can plug in to evaluate F(2)

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