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Hello, Originally Posted by champrock Separate the integral : if x is between 0 and 1, then [x]=0 if x is between 1 and 2, then [x]=1 so your integral is actually , if if n=0, then the integral is
but its actually [X]^N whcih is most confusing. (mod raised to Nth power). so, it cant be seperated that easily.
Originally Posted by champrock but its actually [X]^N whcih is most confusing. (mod raised to Nth power). so, it cant be seperated that easily. It is... Because x varies from 0 to 1 and from 1 to 2. x in [0,1[ => [x]=0 => [x]^n=0^n=0, if n is not equal to 0. x in [1,2[ => [x]=1 => [x]^n=1^n=1.
hmm.. lets just take an example. assume that n=5 and x=1.5, then 1.5^5 = 7.59..
Let be an integer then Hence, for it's which is the value of the integral.
Originally Posted by champrock hmm.. lets just take an example. assume that n=5 and x=1.5, then 1.5^5 = 7.59.. But you're working with the greatest integer function ! It's [x]^n, not [x^n], that's certainly not the same... what I showed you gives the exact same result as Krizalid. (apart from the case n=0)
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