. What is the exact value of ? Give your answer as a fraction or whole number.

I split the fraction, into two fractions, using partial fractions method, to get

$\displaystyle \int^2_0 \frac{2}{x+4} -\frac{2}{x+5} $

= $\displaystyle ln(x+4) - ln(x+5) $

$\displaystyle ln\frac{x+4}{x+5} $

x=2

x=0

$\displaystyle ln\frac{6}{7} - ln\frac{4}{5} $

$\displaystyle ln \frac{30}{28} = 0.06899 $

is the the value of k?