`int_(-3)^(3)x^(8){x^(11)}dx` is equal to (where {.} is the fractional part of `x`)

Options

A. `3^(8`
B. `3^(7)`
C. `3^(9)`
D. none of these

Answer

B

Explanation

`I=int_(-3)^(3)x^(8){x^(11)}dx`
Replacing `x` by `-x` we have `I=int_(-3)^(3)x^(8){-x^(11)}dx`
Adding 1 and 2 we get
`2I=int_(-3)^(3)x^(8)({x^(11)}+{-x^(11)})xdx=2int_(0)^(3)x^(8)dx`
`=2((x^(9))/9)_(0)^(3)=2.3^(7)`
or `I=3^(7)` [As `{x}+{-x}=1` for `x` is not an integer ]