Let I = int_a^b (x^4 - 2x^2) dx. If I is mini | vedclass

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(D) Let $f(x) = x^4 - 2x^2$. To minimize the integral $I = \int_a^b f(x) dx$,we need to integrate over the region where $f(x)$ is negative.$f(x) = x^2

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

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(D) Let $f(x) = x^4 - 2x^2$. To minimize the integral $I = \int_a^b f(x) dx$,we need to integrate over the region where $f(x)$ is negative.$f(x) = x^2(x^2 - 2) = x^2(x - \sqrt{2})(x + \sqrt{2})$.The function $f(x)$ is negative in the interval $(-\sqrt{2}, \sqrt{2})$.Since the integral of a negative function over its entire negative region yields the minimum possible value,we set $a = -\sqrt{2}$ and $b = \sqrt{2}$.Thus,the ordered pair $(a, b)$ is $(-\sqrt{2}, \sqrt{2})$.

Let $I = \int_a^b (x^4 - 2x^2) dx$. If $I$ is minimum,then the ordered pair $(a, b)$ is

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