Question

Find the area of ​​the function f (x) = √x-2.​

Answer 1

We are given that  $f(x)=\sqrt{x} -2$ .

$f(x)=y$

$y=\sqrt{x} -2$

Now let us evaluate  $f(0)$ .

$y=\sqrt{0} -2\\y=-2$

Now let the to limits be -2 and 0.

$Area=\int\limits^0_{-2} {(\sqrt{x} -2)} \, dx$

$Area=\int\limits^0_{-2} {(\sqrt{x} )} \, dx-\int\limits^0_{-2} {(2)} \, dx$               ( $\int\limits {x^{\frac{1}{2} } \, dx$ = $2\frac{x^\frac{3}{2} }{3}$ )

$Area=|\frac{2x\sqrt{x} }{3} |^0_{-2}-|2x|^0_{-2}$          

$Area=\frac{-4\sqrt{2}i }{3} -(-4)$              (if one limit is 0 then   $|x|^n_0=n$ )

        $=\frac{12-4\sqrt{2}i }{3}$