Question

Let $f (x)=g (1) x^2+x g^{\prime} x+g^{\prime \prime} (x)$ and $g (x)$ $=x^2+x f^{\prime} (1)+f^{\prime \prime} (2)\,$, then area bounded by $y=g (x)$ and $x$-axis is

• A. $9$
• B. $\frac{9}{2}$
• C. $\frac{27}{2}$
• D. $27$

Answer 1

Answer: (B)

Clearly, $f\left(x\right)=2-3x$ and $g\left(x\right)=x^{2}-3x$
$g\left(x\right)=$
Area $=\left|\int\limits _{0}^{3} \left(x^{2} - 3 x\right) d x\right|= \frac{x^{3}}{3} - \frac{3 x^{2}}{2} |^{3}_{0}$
$=\left|9 - \frac{27}{2}\right|=\left|\frac{- 9}{2}\right|=\frac{9}{2}$ .