Question

Solve
$-{\int }_{-4}^{-3}\sqrt{-\left(x+3\right)}dx$

Answer 1

$-{\int }_{-4}^{-3}\sqrt{-(x+3)}dxput,t^2=-(x+3)hence,dx=-2tdtandatx=-3;t=0andatx=-4;t=1Hence,-{\int }_1^0-2t\sqrt{t^2}dt$

$=2{\int }_1^0{t}^{2}dt$

$=2{\left[\frac{t^3}{3}\right]}_1^0$

$=2[0-\frac{1}{3}]$

$=-\frac{2}{3}$