Question

The area of the region formed by the curve $\sqrt{x}+\sqrt{y}=2$ between co-ordinate axes is

• A. $\frac{4}{3}$
• B. $\frac{8}{3}$
• C. $\frac{16}{3}$
• D. $\frac{5}{3}$

Answer 1

The correct option is B $\frac{8}{3}$

$\sqrt{x}+\sqrt{y}=2$

$y=(2-\sqrt{x}{)}^2$

$\stackrel{4}{\underset{0}{\int }}[4+x-2(2\left)\right(\sqrt{x}\left)\right]dx$

${[4x+\frac{x^2}{2}-4\left[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]]}_0^4$

$4\left(4\right)+\frac{(4{)}^2}{2}-\frac{4\times 2}{3}\left(2^2\frac{3}{2}\right)-\left(0\right)$

$16+8-\frac{8}{3}\times 8=24-\frac{64}{3}$

$=\frac{72-64}{3}=\frac{8}{3}$