question_answer

Let \[I=\int{_{a}^{b}({{x}^{4}}-2{{x}^{2}})dx.}\]If I is minimum then the ordered pair (a, b) is:

A) \[\left( 0,\sqrt{2} \right)\]             

B)  \[\left( -\sqrt{2},0 \right)\]

C) \[\left( \sqrt{2},-\sqrt{2} \right)\]              

D) \[\left( -\sqrt{2},-\sqrt{2} \right)\]

Correct Answer: D

Solution :

\[\int\limits_{a}^{b}{\left( {{x}^{4}}-2{{x}^{2}} \right)dx}\]

From figure min area is \[\left( -\sqrt{2},\sqrt{2} \right).\]