5.4 Indefinite Integrals and the Net Change Theorem/33

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \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{align} }