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If f(x) = x [x], then for any real numbe...

If `f(x) = x [x]`, then for any real number a and b with `a lt b`, then value of `int_(a)^(b) f (x) dx` equals

A

`(1)/(3) (|b|^(3) - |a|^(3) )`

B

`(1)/(3) |b^(3) -a^(3) |`

C

`(1)/(3) (a^(3) + b^(3) )`

D

`(1)/(3) (a^(3) -b^(3) )`

Text Solution

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The correct Answer is:
B
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Knowledge Check

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    A
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    B
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    A
    `(1)/(2) (a^(2) +b^(2))`
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    `(1)/(3) (b^(2)-a^(2))`
    C
    `(1)/(3) (a^(3) +b^(3))`
    D
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