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IfI=int(-20pi)^(20pi)|sinx|[sinx]dx(w h ...

`IfI=int_(-20pi)^(20pi)|sinx|[sinx]dx(w h e r e[dot]` denotes the greatest integer function), then the value of `I` is `-40` (b) 40 (c) 20 (d) `-20`

A

`-40`

B

`40`

C

`20`

D

`-20`

Text Solution

Verified by Experts

The correct Answer is:
A
`int_(-20pi)^(20pi)|sinx|[sinx]dx=int_(0)^(20pi)|sinx|([sinx]+[-sinx])dx`
`=-20int_(0)^(pi)(sinx)dx`
`=-20(=cosx)_(0)^(pi)`
`=20(2)`
`=-40`
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