# Math Help - Antidifferentiation problem

1. ## Antidifferentiation problem

If f(x) = (x+1)^2 and F(1) = 2, find F(x).

I can't get the answer. Could someone explain to to me? And also, what is the difference between f(x) and F(x)??

2. I assume that $F(x)$ is the antiderivative of $f(x)$.

So if $f(x) = (x + 1)^2 = x^2 + 2x + 1$ then

$F(x) = \int{x^2 + 2x + 1\,dx}$

$= \frac{1}{3}x^3 + x^2 + x + C$.

You know that $F(1) = 2$, so

$2 = \frac{1}{3}(1)^3 + 1^2 + 1 + C$

$2 = \frac{1}{3} + 1 + 1 + C$

$2 = \frac{7}{3} + C$

$C = -\frac{1}{3}$.

Therefore $F(x) = \frac{1}{3}x^3 + x^2 + x - \frac{1}{3}$.

3. thanks!!