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 $=\left|\underset{0}{\overset{3}{\int }}\left(x^2-3x\right)dx\right|=\frac{x^3}{3}-\frac{3x^2}{2}{|}_0^3$
$=\left|9-\frac{27}{2}\right|=\left|\frac{-9}{2}\right|=\frac{9}{2}$ .