Question

The area between the curve $y = 4 + 3x - x^{2}$ and x-axis is

• A. $\frac{125}{6}$ sq. units
• B. $\frac{125}{3}$ sq. units
• C. $\frac{125}{2}$ sq. units
• D. none of these

Answer 1

Answer: (A)

We have, $y = 4 + 3x - x^{2}$, a parabola
Putting $y = 0$, we get $x^{2} - 3x - 4 = 0$
$\Rightarrow \quad\left(x-4\right)\left(x+1\right)=0 \, \Rightarrow \quad x=-1$ or $x = 4$
$\therefore \quad$ Required area $= \int\limits_{-1}^{4}\left(4+3x-x^{2}\right)dx$
$=\left[4x+\frac{3x^{2}}{2}-\frac{x^{3}}{3}\right]_{-1}^{4}=\frac{125}{6}$ sq. units