Solve this following


Let $I=\int_{a}^{b}\left(x^{4}-2 x^{2}\right) d x$. If I is minimum then

the ordered pair (a, b) is :


  1. $(-\sqrt{2}, 0)$

  2. $(-\sqrt{2}, \sqrt{2})$

  3. $(0, \sqrt{2})$

  4. $(\sqrt{2},-\sqrt{2})$

Correct Option: , 2


Let $f(x)=x^{2}\left(x^{2}-2\right)$

As long as $f(x)$ lie below the $x$-axis, definite integral will remain negative,

so correct value of $(a, b)$ is $(-\sqrt{2}, \sqrt{2})$ for minimum of I


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