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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 _________.

A

`(0, sqrt2)`

B

`(- sqrt(2) , sqrt(2) )`

C

`(- sqrt(6) , sqrt(6) )`

D

`(- 2 sqrt , 0 )`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x) = x^2 (x^2 - 6) = x^2 (x - sqrt6) ( x + sqt6)`
sign scheme of f(x)

For integral to be minimum the graph should be below x - axis
`(a,b) -= (- sqrt6, sqrt6) `
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