Question

The area bounded by the coordinate axes and the curve $\sqrt{x}+\sqrt{y}=1$, is

• A. 1 square unit
• B. $\frac{1}{2}$ square unit
• C. $\frac{1}{3}$ square unit
• D. $\frac{1}{6}$ square unit

Answer 1

Answer: (D)

$\frac{1}{6}$ square unit

Solution:

$\therefore$ required area $=\stackrel{1}{\underset{0}{\int }}(1-\sqrt{x}{)}^{2}dx$

$=\stackrel{1}{\underset{0}{\int }}(1-2\sqrt{x}+x)dx$

$={[x-2.\frac{x^{3/2}}{3/2}+\frac{x^2}{2}]}_0^1$

$=1-2.\frac{2}{3}+\frac{1}{2}$

$=1-\frac{4}{3}+\frac{1}{2}=\frac{1}{6}$ square units.

Hence, D is the correct option.