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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!
 one year ago
 one year 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!
 one year ago
 one year ago

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CallistoBest ResponseYou've already chosen the best response.2
\[\int x^{n}dx = \frac{1}{n+1}x^{n+1}+C\]
 one year ago

thomas5267Best ResponseYou've already chosen the best response.1
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!?
 one year ago

CallistoBest ResponseYou've already chosen the best response.2
lol I see your point!!
 one year ago

CallistoBest ResponseYou've already chosen the best response.2
Is it a quiz? homework question?
 one year ago

thomas5267Best ResponseYou've already chosen the best response.1
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."
 one year ago

CallistoBest ResponseYou've already chosen the best response.2
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).
 one year ago

CallistoBest ResponseYou've already chosen the best response.2
Yay! @mukushla comes to save us :P
 one year ago

thomas5267Best ResponseYou've already chosen the best response.1
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?
 one year ago

CallistoBest ResponseYou've already chosen the best response.2
English :S and Maths :S
 one year ago

CallistoBest ResponseYou've already chosen the best response.2
I'm sorry, I'm too careless!!
 one year ago

thomas5267Best ResponseYou've already chosen the best response.1
WTF? Playing with words in Maths assignment? YOU WIN! *ragequit*
 one year ago
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