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Math Help - General Antiderivatives

  1. #1
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    General Antiderivatives

    Just got this question wrong, I make a mistake somewhere and I need some pointing out where to where it is. Heres the problem first

    Find the most general antiderivative of the function
    Alright.. Here's my work:

    First I converted the cube root x^2 and sqrt x^9 to :

    f(x) = x^2/3 - x^9/2

    Then using the antiderivative rule of x^(n+1)/n+1 , I got:

    f(x) = (x^5/3) / (5/3) - (x^11/2) / (11/2) + C

    simplifying that I get :

    3/5x^(5/3) - 2/11x^(11/2) + C

    ... I ended up getting the answer wrong

    Help is greatly appreciated
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by endiv View Post
    Just got this question wrong, I make a mistake somewhere and I need some pointing out where to where it is. Heres the problem first

    Alright.. Here's my work:

    First I converted the cube root x^2 and sqrt x^9 to :

    f(x) = x^2/3 - x^9/2

    Then using the antiderivative rule of x^(n+1)/n+1 , I got:

    f(x) = (x^5/3) / (5/3) - (x^11/2) / (11/2) + C

    simplifying that I get :

    3/5x^(5/3) - 2/11x^(11/2) + C

    ... I ended up getting the answer wrong

    Help is greatly appreciated
    your answer is correct. the integral is \frac 35x^{\frac 53} - \frac 2{11}x^{\frac {11}2} + C
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  3. #3
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    \begin{gathered}<br />
  f'(x) = \sqrt[3]{{x^2 }} - \sqrt {x^9 }  = x^{\frac{2}<br />
{3}}  - x^{\frac{9}<br />
{2}}  \hfill \\<br />
  f(x) = \frac{3}<br />
{5}x^{\frac{5}<br />
{3}}  - \frac{2}<br />
{{11}}x^{\frac{{11}}<br />
{2}}  + C \hfill \\ <br />
\end{gathered}
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  4. #4
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    Oh, wow. My mistake was putting a little c instead of a capital C, which resulted my in a wrong answer :|. Thanks!
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by endiv View Post
    Oh, wow. My mistake was putting a little c instead of a capital C, which resulted my in a wrong answer :|. Thanks!
    i don't see why that should make a difference, but ok. maybe whatever you are typing the answer into is case sensitive
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