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Math Help - Finding F(x) (INTEGRAL)

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    Finding F(x) (INTEGRAL)

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

    I don't understand what it's asking. Do I simply find the antiderivative?
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    Quote Originally Posted by Archduke01 View Post
    Consider the function .
    Let be the antiderivative of with .
    Then ?

    I don't understand what it's asking. Do I simply find the antiderivative?
    Yes, F(x) is the antiderivative of f(x).

    And then you use the boundary condition to evaluate the integration constant.
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    I'm doing something wrong. I get -6 x^{-2} /2 + 2 x^{-6} /6.

    Procedure; .

    I separated the 6 and 2, then brought the denominators up getting 6 \int x^{-3} - 2 \int x^{-7}. Do I apply the power rule at this point?
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    Quote Originally Posted by Archduke01 View Post
    I'm doing something wrong. I get -6 x^{-2} /2 + 2 x^{-6} /6.

    Procedure; .

    I separated the 6 and 2, then brought the denominators up getting 6 \int x^{-3} - 2 \int x^{-7}. Do I apply the power rule at this point?
    Your writing of integrals needs work. You can't leave off the dx's.

    It should read 6\int{x^{-3}\,dx} - 2\int{x^{-7}\,dx}.


    But yes, now apply the power rule.
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    I did apply the power rule, and the original answer is the answer I got. It's not correct though.
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    Quote Originally Posted by Prove It View Post
    Your writing of integrals needs work. You can't leave off the dx's.

    It should read 6\int{x^{-3}\,dx} - 2\int{x^{-7}\,dx}.


    But yes, now apply the power rule.
    6\int{x^{-3}\,dx} - 2\int{x^{-7}\,dx} = 6\left(-\frac{1}{2}x^{-2}\right) - 2\left(-\frac{1}{6}x^{-6}\right) + C

     = -\frac{3}{x^2} - \frac{1}{3x^6} + C.
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