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Let [x] denote the largest interger not ...

Let [x] denote the largest interger not exceeding x and `{x}=x-[x]`. Then `int_(0)^(2012) e^(cos (pi{x}))/(e^(cos (pi{x}))+e^(-cos(pi{x})))dx` is equal to -

A

0

B

1006

C

2012

D

`2012 pi`

Text Solution

Verified by Experts

The correct Answer is:
B
`I=2012 underset(0)overset(1)(int) e^(cos pi x)/(e^(cos pi x)+e^(-cos pi x))dx`
using king property `I =2012 underset(0)overset(1)(int) e^(-cos pi x)/(e^(-cos pi x)+e^(cos pi x))dx rArr 2I=2012 rArr I=1006`
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