g ( r ) = ∫ 0 r x 2 + 4 d x d d x ∫ 0 r x 2 + 4 d x d d x ∫ b ( x ) a ( x ) F ( t ) d t = d d x [ b ( x ) ] ⋅ F ( b ( 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]{\frac {d}{dx}}\int _{b(x)}^{a(x)}F(t)dt={\frac {d}{dx}}[b(x)]\cdot F(b(x))\\[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]{\frac {d}{dx}}\int _{b(x)}^{a(x)}F(t)dt={\frac {d}{dx}}[b(x)]\cdot F(b(x))\\[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/47930438b8f69ef835b2eee4f52f2a3896b1aa37)