# Math Help - Function 2

1. ## Function 2

Knowing that $f'(x)=\frac{x+2}{x^2+4x+11}$ and $f(1)=0$ then the value of $f(0)$ is ?

2. Originally Posted by Apprentice123
Knowing that $f'(x)=\frac{x+2}{x^2+4x+11}$ and $f(1)=0$ then the value of $f(0)$ is ?
1. Calculate F(x):

$F(x)=\dfrac12 \cdot \int \left(\dfrac{2x+4}{x^2+4x+11}\right) dx=\dfrac12 \ln(x^2+4x+11)+C$

2. Calculate F(1):

$F(1)=\dfrac12 \ln(1+4+11)+C=2\ln(2)+C = 0~\implies~ C=-2\ln(2)$

3. Calculate F(0):

I'll leave this part for you.