g ( r ) = ∫ 0 r x 2 + 4 d x d d x ∫ 0 r x 2 + 4 d x 1 ⋅ r 2 + 4 − 0 ⋅ 0 2 + 4 = r 2 + 4 {\displaystyle {\begin{aligned}g(r)=\int _{0}^{r}{\sqrt {x^{2}+4}}dx\\[2ex]{\frac {d}{dx}}\int _{0}^{r}{\sqrt {x^{2}+4}}dx\\[2ex]1\cdot {\sqrt {r^{2}+4}}-0\cdot {\sqrt {0^{2}+4}}\\[2ex]={\sqrt {r^{2}}}+{4}\end{aligned}}}
![{\displaystyle {\begin{aligned}g(r)=\int _{0}^{r}{\sqrt {x^{2}+4}}dx\\[2ex]{\frac {d}{dx}}\int _{0}^{r}{\sqrt {x^{2}+4}}dx\\[2ex]1\cdot {\sqrt {r^{2}+4}}-0\cdot {\sqrt {0^{2}+4}}\\[2ex]={\sqrt {r^{2}}}+{4}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/5376c3c7c2c7e2a48637f7fba0cb4f021f0a6215)