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Let I=int(a)^(b)(x^(4)-2x^(2))dx. If I i...

Let `I=int_(a)^(b)(x^(4)-2x^(2))dx`. If I is minimum then the ordered pair (a,b) is `(-sqrtk,sqrtl)`. The value of (k+l) is _________.

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The correct Answer is:
4
`I=int_(a)^(b)(x^(4)-2x^(2))dx`
Consider `f(x)=x^(4)-2x^(2)=x^(2)(x^(2)-2)`
Obviously `int_(a)^(b)(x^(4)-2x^(2))dx` is least when `a=-sqrt2` and `b=sqrt2`
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