Question

Let $f\left(x\right)=x^2-3x+2$ be a function,$\forall x\in R$. On the basis of above in formation, answer the following questions. The area bounded by the curve $f\left(|x|\right)$ and $x$-axis is:

• A. $\frac{2}{5}$ sq. unit
• B. $\frac{5}{2}$ sq. unit
• C. $\frac{3}{5}$ sq. unit
• D. $\frac{1}{3}$ sq. unit

Answer 1

Answer: (D)

$\frac{1}{3}$ sq. unit

$f\left(x\right)=x^2-3x+2$
$f\left(|x|\right)=x^2-3|x|+2$
$=2\left|\stackrel{2}{\underset{1}{\int }}(x^2-3x+2)dx\right|$
$=2[\frac{x^3}{3}-\frac{3x^2}{2}+2x{\mid }_1^2]$
$=2[7/3-3\left[\frac{3}{2}\right]+2]$
$=2[7/3-9/2+2]$
$=1/3squnits.$