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 $f\left(x\right)$ ,the $x$ axis and $y$-axis is:

• A. $\frac{1}{3}$ sq. unit
• B. $\frac{2}{3}$ sq. unit
• C. $\frac{3}{5}$ sq. unit
• D. $\frac{5}{6}$ sq. unit

Answer 1

Answer: (D)

$\frac{5}{6}$ sq. unit

$\stackrel{1}{\underset{0}{\int }}f\left(x\right)dx$
$=\stackrel{1}{\underset{0}{\int }}(x^2-3x+2)dx$
$=\frac{x^3}{3}-\frac{3x^2}{2}+2x{|}_0^1$
$=1/3-3/2+2=\frac{2-9+12}{6}$
$=5/6squnits.$