If `I=int_(-20pi)^(20pi)|sinx|[sinx]dx` (where [.] denotes the greatest integer function) then the value of `I` is
If `I=int_(-20pi)^(20pi)|sinx|[sinx]dx` (where [.] denotes the greatest integer function) then the value of `I` is
A. `-40`
B. `40`
C. `20`
D. `-20`
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Correct Answer - 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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