## Calculus 8th Edition

$2\sqrt5$
We can rewrite this integral as $\int_1^4 (5x^{-1})^{\frac{1}{2}}dx = \int_1^4 5^{\frac{1}{2}}x^{-\frac{1}{2}}dx$ to see that we can treat $5^{\frac{1}{2}}$ as a constant and move it out of the integrand, making our integral $(5^{\frac{1}{2}})\int_1^4 x^{-\frac{1}{2}}dx$ instead Evaluating the integral gives us $2x^\frac{1}{2}\big|_1^4$ Substituting in $4$ and $1$ gives us $(2 \sqrt 4 ) - (2 \sqrt 1) = 4 - 2 = 2$ We now multiply our answer by $(5^{\frac{1}{2}})$ and get $2\sqrt5$ as our final answer