Evaluate: $^9{?}_1$ \(\frac{x(2x-3)}{?x}\..

Question 1 Report

Evaluate: $^9{?}_1$ $\frac{x(2x-3)}{?x}$ dx

Answer

$^{9} \int_{1}$ $\frac{x (2 x - 3)}{\sqrt x}$ dx = $\frac{2 x^{2} - 3 x)}{x^{1 / 2}}$

$^{- 1 / 2}$ (2x $^{2}$ - 3x)

= 2x $^{3 / 2}$ - 3x $^{1 / 2}$

= $\frac{2 x^{3 / 2}}{3 / 2 + 1}$ - $\frac{3 x^{1 / 2}}{1 / 2 + 1}$

= $\frac{2 x^{3 / 2}}{5 / 2}$ - $\frac{3 x^{1 / 2}}{3 / 2}$

= $^{9} \int_{1}$ [ $\frac{4 x^{3 / 2}}{5}$ - $\frac{6 x^{1 / 2}}{3}$ ]

[ $\frac{4 (9)^{3 / 2}}{5}$ - $\frac{6^{(} 9) 1 / 2}{3}$ ] - [ $\frac{4 (9)^{1 / 2}}{5}$ - $\frac{6 (1)^{1 / 2}}{3}$ ]

= [ $\frac{4 (27)}{5}$ - $\frac{6 (3)}{3}$ - [ $\frac{4}{5}$ - 2 ]

= [ $\frac{108}{5}$ - 2 ] - [ $\frac{6}{5}$ ]

= $\frac{78}{5}$ + $\frac{6}{5}$ = $\frac{84}{5}$

$^{9} \int_{1}$

16 $^{4 / 5}$

Answer Details