Question

integral de ( x-1) / sqrt (x) de [1,3] ​

Answer 1

Respuesta:

Explicación:

$\int\limits^3_1 {\frac{x-1}{\sqrt{x} } } \, dx$

$\int\limits^3_1 {(x-1)x^{-1/2} } \, dx \\\\\\\int\limits^3_1 {x^{1/2} -x^{-1/2} } \, dx \\\\\\ \frac{x^{3/2}}{3/2} - \frac{x^{1/2}}{1/2} , [1,3] \\\\\\\frac{2\sqrt{x^{3} } }{3} - 2\sqrt{x} , [1,3]$

$( \frac{2\sqrt{3^{3} } }{3} - 2\sqrt{3} )-( \frac{2\sqrt{1^{3} } }{3} - 2\sqrt{1} )\\\\ ( \frac{6\sqrt{3} }{3} - 2\sqrt{3} )-( \frac{2 }{3} - 2)\\\\(2\sqrt{3} -2\sqrt{3} ) - ( -\frac{4}{3} ) \\\\\frac{4}{3}$