Question

The area bounded by $yu=x+2,y=2-x$ and the $x$-axis is ( in square units) :

• A. $1$
• B. $2$
• C. $4$
• D. $6$
• E. $8$

Answer 1

Answer: (C)

$4$

Given lines are $yu=x+2,y=2-x$
The intersection point is
$2-x=x+2\Rightarrow 2x=0$
$\Rightarrow x=0\Rightarrow y=2$
Therefore, intersection point is $(0,2)$.
Hence, required shaded region $=$ Area of shaded region $AOB$ $+$ Area of shaded region $BOC$
${\int }_{-2}^{0}ydx+{\int }_0^{2}ydx$
${\int }_{-2}^0(x+2)dx+{\int }_a^2(2-x)dx$
$={[\frac{x^2}{2}+2x]}_{-2}^0+{[2x-\frac{x^2}{2}]}_0^2$
$=[0+0-(\frac{4}{2}-)]+[4-\frac{4}{2}]$
$=2+2=4$ sq units