Question

Area included between curves $y=x^2-3x+2$ and $y=-x^2+3x-2$ is

• A. $\frac{1}{6}$ sq unit
• B. $\frac{1}{2}$ sq unit
• C. $1$ sq unit
• D. $\frac{1}{3}$ sq unit
• E. None of these

Answer 1

The correct option is D

$\frac{1}{3}$ sq unit

Explanation for the correct option:

Draw the graph of curves $y=x^2-3x+2$ and $y=-x^2+3x-2$:

From the figure, we can see

Given curves are intersecting at points $x=1$ and $x=2$

$\therefore$The required area $=2{\int }_1^2\left(-x+3x-2\right)dx$

$$\begin{gathered} =2{\left[-\frac{x^3}{3}+\frac{3x^2}{2}-2x\right]}_1^2 \\ =2\left[-\frac{8}{3}+6-4-\left(-\frac{1}{3}+\frac{3}{2}-2\right)\right] \\ =2\left[-\frac{8}{3}+2+\frac{5}{6}\right] \\ =\frac{1}{3} \end{gathered}$$

Thus, the area included between the given curves is $\frac{\mathbf{1}}{\mathbf{3}}$ sq unit

Hence, Option ‘D’ is Correct.