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what is the integrand of [x2-1] upperlimit-2,lower limit-0 where [ ] represents greatest integer function
From the graph , y+1 = x2 , we can say
between x=(0,1) y takes value of -1
x=(1,1.414) y takes value of 0
x=(1.414,1.732) y takes value of 1
x=(1.732,2) y takes value of 2
integrating in these limits gives
I = int ( -dx) + int ( 0*dx) + int ( dx) + int ( 2*dx) with above limits respecively
I = 1.732 - 1.414 = 0.218
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regards
Ramesh
graph of [x^(2)-1]
integration is the area under the graph so its basically the area of the rectangle tht is 1*-1=1
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