1.

The value of int_(-20pi)^(20 pi) [ sin x + cos x] dxis(where [.] denotes greatest integer function)

Answer»

`10 pi`
`-20 pi`
`20 pi`
`-10 pi`

SOLUTION :`I=20[int_(0)^(pi//2)1dx+int_(pi//2)^(3pi//4)0dx+int_(3pi//4)^(pi)-1dx+int_(pi)^(3pi//2)-2dx+int_(3pi//2)^(7pi//4)-1dx+int_(7pi//4)^(2pi)0dx]`
`=20XX[(pi)/(2)-pi+(3pi)/(4)-2xx(3pi)/(2)+2pi-(7pi)/(4)+(3pi)/(2)]=20xx-pi=-20pi`


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