Evaluate `int_(1)^(e^(6))[(logx)/3]dx,` where [.] denotes the greatest integer function.

Evaluate `int_(1)^(e^(6))[(logx)/3]dx,` where [.] denotes the greatest

1.	Evaluate `int_(1)^(e^(6))[(logx)/3]dx,` where [.] denotes the greatest integer function.
Answer» Correct Answer - `(e^(6)-e^(3))` When `1ltxlte^(3),[(logx)/3]=0` and when `e^(3)ltxlte^(6),[(logx)/3]=1` `:. int_(1)^(e^(6))[(logx)/3]dx=int_(1)^(e^(3))[(logx)/3]dx+int_(e^(3))^(e^(6))[(logx)/3]dx` `=int_(1)^(e^(3)) 0dx+int_(e^(3))^(e^(6))1dx=(e^(6)-e^(3))`

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