Question

Let $f\left(x\right)=x^2-5x+6$ be a function $\forall x\in R$.
On the basis of the above information, answer the following question.
The area bounded by the curve $f\left(|x|\right)$ and $x-$axis, in square units is

• A. $\frac{29}{3}$
• B. $\frac{28}{3}$
• C. $\frac{15}{4}$
• D. $\frac{19}{3}$

Answer 1

The correct option is B $\frac{28}{3}$

$f\left(\left|x\right|\right)={\left|x\right|}^2-5\left|x\right|+6$
The point at which $y=f\left(x\right)$ meets the $x-$axis are obtained by putting $y=0$
Therefore,

${\left|x\right|}^2-5\left|x\right|+6=0$, $(\left|x\right|-2)(\left|x\right|-3)=0$
$\left|x\right|=2$, $\left|x\right|=3$ $\therefore$ $x=\pm 2$, $x=\pm 3$

$(2,0),(3,0),(-2,0),(-3,0)$ are points on $x-$axis.
$\therefore$ Required area $=2{\int }_0^{2}ydx=2\times \frac{14}{3}=\frac{28}{3}$ square units.