ISI2017-DCG-29

Question

The area (in square unit) of the portion enclosed by the curve $\sqrt{2x}+ \sqrt{2y} = 2 \sqrt{3}$ and the axes of reference is

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The above equation can be re-written as follows:

$\sqrt{x} + \sqrt{y} = \sqrt{6}$

This depicts the graphical notation of the above curve:

The curve can be re-written as follows:

$\sqrt{y} = \sqrt{6} - \sqrt{x}$

$y = 6 + x + \left ( 2\ast \sqrt{6}\ast \sqrt{x}\right )$

The value of x varies from x = 0  to x = 6

Area under the curve  = $\int_{0}^{6}\left [6 + x + \left ( 2\ast \sqrt{6}\ast \sqrt{x}\right )\right ]dx$

                                       =  $\left [ 6\ast x + {\frac{x^{2}}{2}} + 3\ast\sqrt{6}\ast x^{\frac{3}{2}}\right ]$

On computing this, you get Area = 6.

Thus, answer is option (C).