Question

The area bounded by the line $y=|x-2|,\left|x\right|=3$ and $y=0$ is

• A. 13 unit${}^2$
• B. 5 unit${}^2$
• C. 9 unit${}^2$
• D. 7 unit${}^2$

Answer 1

The correct option is A 13 unit${}^2$

The graph of $y=x$ cuts the x axis at x=2.
For $x<2$
$y=2-x$
Hence area between -3 to 2 will be
$={\int }_{-3}^2(2-x).dx$
$=\frac{5\times 5}{2}$ ...(area of right angled triangle with coordinates (2,0),(-3,0)(-3,5)).
$=\frac{25}{2}$ ...(i)
And area bounded by f(x) between 2 and 3
$={\int }_2^{3}x-2.dx$
$=\frac{1\times 1}{2}$ ...(area of right angled triangle with coordinates (2,0),(3,0)(3,1)).
$=\frac{1}{2}$ ...(ii)
Hence the total area bounded by the curve between -3 and 3 is equal to
$=i+ii$
$=\frac{25}{2}+\frac{1}{2}$
$=13$ sq units.