∫ 1 4 5 x d y = ∫ 1 4 5 x d x = 5 ∫ 1 4 x − 1 2 d x = 2 5 x 1 2 | 1 4 = [ 2 5 4 ] − [ 2 5 1 ] = 4 5 − 2 5 = 2 5 {\displaystyle {\begin{aligned}\int _{1}^{4}{\sqrt {\frac {5}{x}}}dy&=\int _{1}^{4}{\frac {\sqrt {5}}{\sqrt {x}}}dx={\sqrt {5}}\int _{1}^{4}x^{-{\frac {1}{2}}}dx\\[2ex]&=2{\sqrt {5}}x^{\frac {1}{2}}{\bigg |}_{1}^{4}\\[2ex]&=[2{\sqrt {5}}{\sqrt {4}}]-[2{\sqrt {5}}{\sqrt {1}}]=4{\sqrt {5}}-2{\sqrt {5}}\\[2ex]&=2{\sqrt {5}}\end{aligned}}}
![{\displaystyle {\begin{aligned}\int _{1}^{4}{\sqrt {\frac {5}{x}}}dy&=\int _{1}^{4}{\frac {\sqrt {5}}{\sqrt {x}}}dx={\sqrt {5}}\int _{1}^{4}x^{-{\frac {1}{2}}}dx\\[2ex]&=2{\sqrt {5}}x^{\frac {1}{2}}{\bigg |}_{1}^{4}\\[2ex]&=[2{\sqrt {5}}{\sqrt {4}}]-[2{\sqrt {5}}{\sqrt {1}}]=4{\sqrt {5}}-2{\sqrt {5}}\\[2ex]&=2{\sqrt {5}}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/6ed4dda3c0671d278be3d931ee7adb2ef8514117)