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Evaluate: int0^x[cost]dtw h e r en in (2...

Evaluate: `int_0^x[cost]dtw h e r en in (2npi,(4n+1pi/2),n in N ,a n d[dot]` denotes the greatest integer function.

Text Solution

Verified by Experts

Let
`I=int_(0)^(x)[cos t] dt`
`=int_(0)^(2npi)[cost]dt+int_(2pi)^(x)[cost]dt`
`=nint_(0)^(2pi)[cost]dt+int_(2npi)^(x)[cost]dt`
`=-npi+int_(2npi)^(x)0 dt`
`=-npi`
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