Question

The area bounded by $y=-|x|+3,x=0,y=0$ and $x=2,$ is

• A. $\frac{7}{2}\text{sq. units}$
• B. $4\text{sq. units}$
• C. $\frac{11}{2}\text{sq. units}$
• D. $6\text{sq. units}$

Answer 1

The correct option is B $4\text{sq. units}$

We get $y=-|x|$ by inverting the graph $y=|x|$ with respect to $x-$ axis.



For $y=-|x|+3,$ we move the curve up by $3$ units.


From the graph we can see that,
$x=2$ intersects $y=-|x|+3$ at point $(2,1).$

$\therefore$ Required area $=$ Area of trapezium
$=\frac{1}{2}\times (3+1)\times 2=4\text{sq. units}$