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

• A. $\frac{12}{3}$
• B. $\frac{14}{3}$
• C. $\frac{8}{3}$
• D. $\frac{7}{3}$

Answer 1

The correct option is B $\frac{14}{3}$

$\because f\left(x\right)=x^2-5x+6=(x-2)(x-3)$
$\therefore$ Required area ${\int }_0^2(x^2-5x+6)dx$
$={(\frac{x^3}{3}-\frac{5x^2}{2}+6x)}_0^2$
$=\frac{8}{3}-10+12=\frac{14}{3}$square units