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!

Question

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!

callisto · Answer

$$\int x^{n}dx = \frac{1}{n+1}x^{n+1}+C$$

thomas5267 · Answer

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!?

callisto · Answer

lol I see your point!!

callisto · Answer

Is it a quiz? homework question?

thomas5267 · Answer

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."

callisto · Answer

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).

callisto · Answer

Yay! @mukushla comes to save us :P

thomas5267 · Answer

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?

callisto · Answer

English :S and Maths :S

callisto · Answer

I'm sorry, I'm too careless!!

thomas5267 · Answer

WTF?  Playing with words in Maths assignment?  YOU WIN!  *ragequit*

callisto · Answer

Language :S