Q240 / 270 · NDA 2015 (Phase 2) · Mathematics
The area bounded by the coordinate axes and the curve $\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}=1$, is
- A1 square unit
- B1/2 square unit
- C1/3 square unit
- Correct answerD1/6 square unit
Solution
Area $=\int \mathrm{ydx}$
$=\int_0^1(1-\sqrt{x})^2 d x$
[ $\because$ curve makes the intercept of 1 on both axes]
$\begin{aligned}
& =\int_0^1(1+x-2 \sqrt{x}) d x \\
& =[x]_0^1+\frac{1}{2}\left[x^2\right]_0^1-\frac{4}{3}\left[x^{\frac{3}{2}}\right]_0^1 \\
& =1+\frac{1}{2}-\frac{4}{3} \\
& =\frac{3}{2}-\frac{4}{3}=\frac{1}{6} \text { sq unit }
\end{aligned}$
Hence, the correct answer is option: 'D'.