Question

The area included between curves $y = x^{2} - 3x + 2$ and $y = -x^{2} + 3x - 2$ is

• A. $\frac{1}{6}$ sq. units
• B. $\frac{1}{2}$ sq. units
• C. $1$ sq. unit
• D. $\frac{1}{3}$ sq. units

Answer 1

Answer: (D)

Required area $= 2\int\limits_{1}^{2} \left(-x^{2} +3x -2\right) dx $

$ = 2\left[-\frac{x^{3}}{3} + \frac{3x^{2}}{2} -2x\right]_{1}^{2} $
$ = 2\left[-\frac{8}{3} +6 - 4 -\left(-\frac{1}{3} +\frac{3}{2} -2\right)\right] $
$ = 2\left[-\frac{8}{3} + 2 + \frac{5}{6} \right]$
$=\frac{1}{3}$ sq. units