Let I = _a^b ( x^4 - 2 x^2 )dx . If I is minimum then the ordered… - Vidyadip

MCQ

Let $I = \int_a^b {\left( {{x^4} - 2{x^2}} \right)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
$\left( {\sqrt 2 , - \sqrt 2 } \right)$
✓
$\left( {-\sqrt 2 , \sqrt 2 } \right)$

✓

Answer

Correct option: D.

$\left( {-\sqrt 2 , \sqrt 2 } \right)$

d
$\int\limits_a^b {\left( {{x^4} - 2{x^2}} \right)dx} $

From figure min area is $(-\sqrt{2}, \sqrt{2})$

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