Question

Assertion :If $f\left(x\right)=(x-1)(x-2)(x-3),$ then area enclosed by $\left|f\left(x\right)\right|$ between the lines $x=2.2,x=2.8$ and $x-$axis is equal to ${\int }_{2.2}^{2.8}(x-1)(x-2)(x-3)dx$ Reason: $(x-1)(x-2)(x-3)\le 0$ for all $x\in [2.2,2.8]$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

It is clear from the figure for $x\in [2.2,2.8]$
$\Rightarrow (x-1)(x-2)(x-3)\le 0$
Required Area $={\int }_{2.2}^{2.8}(x-1)(x-2)(3-x)dx$