5.3 The Fundamental Theorem of Calculus/10

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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))-{\frac {d}{dx}}[a(x)]\cdot F(a(x))\\[2ex]1\cdot {\sqrt {r^{2}+4}}-0\cdot {\sqrt {0^{2}+4}}\\[2ex]={\sqrt {r^{2}+4}}\end{aligned}}}