Question

The area enclosed by $2\left|x\right|+3|y|\le 6$ is

• A. 3 sq. units
• B. 4 sq. units
• C. 12 sq. units
• D. None of theses

Answer 1

The correct option is C 12 sq. units

$2\left|x\right|+3\left|y\right|\le 6$

$2x+3y\le 6$

$\Rightarrow 3y=6-2x$

$\Rightarrow y=\frac{6-2x}{3}$

Required area$=4{\int }_0^{3}ydx$

$=4{\int }_0^3\frac{6-2x}{3}dx$

$=\frac{4}{3}{\int }_0^3(6-2x)dx$

$=\frac{4}{3}{[6x-\frac{2x^2}{2}]}_0^3$

$=\frac{4}{3}{[6x-x^2]}_0^3$

$=\frac{4}{3}[(18-9)-(0-0)]$

$=\frac{4}{3}\times 9=12$sq.units.