If `[dot]` denotes the greatest integer function, then find the value of `int_1^2[3x]dx`

Explanation

`I=int_1^2[3x]dx`

let `3x=t`

`3dx=dt`


`I=1/3 int_3^6[t]dt`

`I=1/3 [int_3^4[t]dt+int_4^5[t]dt+int_5^6[t]dt]`

`I=1/3 [3int_3^4dt+4int_4^5dt+5int_5^6dt]`

`I=1/3[3(4-3)+4(5-4)+5(6-5)]`

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