Question

Let $f\left(x\right)=x^2-3x+2$ then area bounded by the curve $f\left(\left|x\right|\right)$ (in square units) and x-axis is

• A. $\frac{1}{3}$
• B. $\frac{5}{6}$
• C. $\frac{5}{3}$
• D. None of these

Answer 1

The correct option is C $\frac{5}{3}$

If the area bounded by the curve $y=f\left(x\right)$, x-axis and y-axis be $a$ square units then area bounded by $f\left(\left|x\right|\right)$ and x-axis be twice of $a$
Shaded Area $={\int }_0^{1}f\left(x\right)dx=\frac{5}{6}sq.units$
again Graph of $f\left(\left|x\right|\right)$
$\therefore$ Required Area bounded by $f\left(\left|x\right|\right)$
$={\int }_{-1}^{1}f\left(x\right)dx=2{\int }_0^{1}f\left(x\right)dx=2.\frac{5}{6}=\frac{5}{3}squnits$