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 $|f\left(|x|\right)|$ between $2\le \left|x\right|\le 3$ & x-axis is (in square units)

• A. $\frac{2}{3}$
• B. $\frac{14}{3}$
• C. $\frac{1}{6}$
• D. $\frac{1}{3}$

Answer 1

Answer: (D)

$\frac{1}{3}$

The graph of $\left|f\left(\left|x\right|\right)\right|$ we have $2\le \left|x\right|\le 3$
$\Rightarrow$ $xϵ[-3,-2]\cup [2,3]$
$\therefore$ Area $=2\left|{\int }_2^{3}f\left(x\right)dx\right|$
$\therefore$ Required Area $=2\left|{\int }_2^3(x^2-5x+6)dx\right|=2\times \frac{1}{6}=\frac{1}{3}$