Question

The area of the region bounded by the curve $y=4+3x-x^2$ and $x-$ axis is

• A. $\left(\frac{125}{3}\right)squnits$
• B. $\left(\frac{125}{6}\right)squnits$
• C. $\left(\frac{125}{4}\right)squnits$
• D. None of these

Answer 1

Answer: (B)

Given equation of curves are
$y=4+3x-x^2$ and $y=0$ .
On solving these equations, we get
$x=-1,4$ $\therefore$
Required area $={\int }_{-1}^{4}ydx$
$={\int }_{-1}^4(4+3x-x^2)dx$
$={\left[4x+\frac{3x^2}{2}-\frac{x^3}{3}\right]}_{-1}^4$
$=16+24-\frac{64}{3}+4-\frac{3}{2}-\frac{1}{3}$
$=44-\frac{65}{3}-\frac{3}{2}$
$=\frac{264-130-9}{6}$
$=\frac{125}{6}squnit$