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thomas5267

  • 3 years ago

If \(3x^2+4\) is an antiderivative of \(f(x)\), evaluate the indefinite integral \[F(x)=\int f(x)\,dx\] A: \(F(x)=x^3+4x+C\) B: \(F(x) = 3x^2+C\) C: \(F(x) = 3(x + C)^2+4\) D: \(F(x) = C(3x^2+4)\) E: none of the above Isn't the answer \(3x^2+4\)? That just seems wrong!

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  1. Callisto
    • 3 years ago
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    \[\int x^{n}dx = \frac{1}{n+1}x^{n+1}+C\]

  2. thomas5267
    • 3 years ago
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    OK, but the question is asking for the antiderivative of \(f(x)\), isn't that equals to \(\int f(x) \, dx\)? And the question says that it is \(3x^2+4\). WHAT!? The question has given you the answer!?

  3. Callisto
    • 3 years ago
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    lol I see your point!!

  4. Callisto
    • 3 years ago
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    Is it a quiz? homework question?

  5. thomas5267
    • 3 years ago
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    This is a assignment. If I am correct, \(F(x)=3x^2+4\). So does it equals to \(3x^2+C\)? But it is absolutely weird to use \(C\) in this context. The homework says that "Assume that C is an arbitrary constant throughout this assignment."

  6. Callisto
    • 3 years ago
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    If \(3x^2+4\) is an antiderivative of f(x), so is \(3x^2+5\), \(3x^2+100\), etc. So, generally, \(3x^2+C\) is the antiderivative of f(x).

  7. Callisto
    • 3 years ago
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    Yay! @mukushla comes to save us :P

  8. thomas5267
    • 3 years ago
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    OK. I get the point. \(3x^2+4\) is AN antiderivative of \(f(x)\), i.e. \(3x^2+4\) is one of the antiderivative of \(f(x)\). Therefore, the answer is B! *facepalm* Is this a question on Maths or English?

  9. Callisto
    • 3 years ago
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    English :S and Maths :S

  10. Callisto
    • 3 years ago
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    I'm sorry, I'm too careless!!

  11. thomas5267
    • 3 years ago
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    WTF? Playing with words in Maths assignment? YOU WIN! *ragequit*

  12. Callisto
    • 3 years ago
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    Language :S

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