# What is the net area between f(x) = 1/sqrt(x+1)  and the x-axis over x in [1, 4 ]?

It is $2 \cdot \left(\sqrt{5} - \sqrt{2}\right)$
$A = {\int}_{1}^{4} \frac{1}{\sqrt{x + 1}} \mathrm{dx} = {\left[2 \cdot \sqrt{x + 1}\right]}_{1}^{4} = 2 \cdot \left(\sqrt{5} - \sqrt{2}\right)$