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integral involving greatest integer sin[x....]
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[x2- ] = -4 0<=x< (-3)= -3  (-3)<=x<(-2)= -2 (-2)<=x<(-1)= -1 (-1)<=x<= 0 <=x<(+1)= 1 (+1)<=x<(+2)= 2 (+2)<=x<(+3)= 3 (+3)<=x<(+4)= 4 (+4)<=x<(+5)= 5 (+5)<=x<(+6)= 6 (+6)<=x<Hence integrating x.sin[x2- ] in the above intervals sin[x2-] becomes constant and we are left to integrate x .After simplifying the integral comes out to be I = [(4- )/2].sin4 + (sin5)/2 + [(2--6)/2].sin6Best Wishes |
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Bipin Kumar Dubey Chemical Dept. IIT Kharagpur |
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