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 2 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!
 2 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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Callisto
 2 years ago
Best ResponseYou've already chosen the best response.2\[\int x^{n}dx = \frac{1}{n+1}x^{n+1}+C\]

thomas5267
 2 years ago
Best ResponseYou've already chosen the best response.1OK, 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!?

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.2lol I see your point!!

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.2Is it a quiz? homework question?

thomas5267
 2 years ago
Best ResponseYou've already chosen the best response.1This 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."

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.2If \(3x^2+4\) 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).

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.2Yay! @mukushla comes to save us :P

thomas5267
 2 years ago
Best ResponseYou've already chosen the best response.1OK. 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?

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.2English :S and Maths :S

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.2I'm sorry, I'm too careless!!

thomas5267
 2 years ago
Best ResponseYou've already chosen the best response.1WTF? Playing with words in Maths assignment? YOU WIN! *ragequit*
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