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The value of int(e)^(pi^(2))[log(pi)x]d(...

The value of `int_(e)^(pi^(2))[log_(pi)x]d(log_(e)x)` (where [.] denotes greatest integer function) is

A

`2log_(e)pi`

B

`log_(e)pi`

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
Let `log_(e)x=t`
`I=int_(1)^(log_(e)pi^(2))[log_(pi)e^(t)]dt`
`rArr" "I=int_(1)^(log_(e)pi^(2))[tlog_(pi)e]dt=int_(1)^(log_(e)pi)0dt+int_(log_(e)pi)^(2log_(e)pi)1dt=log_(e)pi`
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