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)??

Thank you for your help.

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- Sep 15th 2010, 10:54 PMKlutzAntidifferentiation 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)??

Thank you for your help. - Sep 15th 2010, 11:01 PMProve It
I assume that $\displaystyle F(x)$ is the antiderivative of $\displaystyle f(x)$.

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

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

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

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

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

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

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

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

Therefore $\displaystyle F(x) = \frac{1}{3}x^3 + x^2 + x - \frac{1}{3}$. - Sep 16th 2010, 01:38 AMKlutz
thanks!!