## thomas5267 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!

1. Callisto

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

2. thomas5267

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

4. Callisto

Is it a quiz? homework question?

5. thomas5267

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

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

Yay! @mukushla comes to save us :P

8. thomas5267

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

English :S and Maths :S

10. Callisto

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

11. thomas5267

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

12. Callisto

Language :S