Which of the following describes the general anti-derivative of a function?
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A. The anti-derivative of f (x) is integral sign f(x)dx = f'(x): , where f ‘(x) is the derivative of f(x).
B. The anti-derivative of f (x) is integral sign f(x)dx = F(x): , where f(x) is the derivative of F(x).
C. The anti-derivative of f (x) is integral sign f(x)dx = f'(x) + C: , where f ‘(x) is the derivative of f(x).
D. The anti-derivative of f (x) is integral sign f(x)dx = F(x) + C : , where f(x) is the derivative of F(x).
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Taking the integral of f(x) should not produce the `derivative f'(x)`.
It should produce the anti-derivative.
That information should allow us to cross off two of our options, do you see which?
yes B and D?
It would eliminate A and C.
See how they're producing a derivative as a result of integrating? That is not good.
So that leaves us with B or D?
They're very similar.
D claims that we should be getting a constant when we integrate.
B does not.
It's one of those two.
Can you remember anything about integrals? :)
Does a constant of integration sound like something familiar, or no?