Question

Let $f\left(x\right)=x^2-3x+2.$ Then which of the following is/are true?
(where $Q_1$ denotes first quadrant)

• A. area bounded by $y=f\left(|x|\right),$ and $x-$axis, and $y-$axis in $Q_1$ is $\frac{5}{6}$ sq. units
• B. area bounded by $y=f\left(|x|\right),$ and $x-$axis is $2$ sq. units
• C. area bounded by $y=f\left(|x|\right),$ between $1\le x\le 2$ and $x-$axis is $\frac{1}{6}$sq. units
• D. area bounded by $y=f\left(|x|\right),$ and $x-$axis is $1$ sq. units

Answer 1

Answer: (A), (B), (C)

area bounded by $y=f\left(|x|\right),$ between $1\le x\le 2$ and $x-$axis is $\frac{1}{6}$sq. units


Area bounded by $y=f\left(|x|\right),$ and $x-$axis, and $y-$axis in $Q_1:$
Required area $=\underset{0}{\overset{1}{\int }}(x^2-3x+2)dx=\frac{5}{6}$

Area bounded by $y=f\left(|x|\right),$ and $x-$axis:
Required area:
$2\left(\underset{0}{\overset{1}{\int }}(x^2-3x+2)dx+\left|\underset{1}{\overset{2}{\int }}(x^2-3x+2)dx\right|\right)=2$

Area bounded by $y=f\left(|x|\right),$ between $1\le x\le 2$ and $x-$axis
Required area:
$=\left|\underset{1}{\overset{2}{\int }}(x^2-3x+2)dx\right|=\frac{1}{6}$