111/alna([x])(a-1)
\int_{0}^{[x]}{a^t/a^[^t^]}dt (a>0), where [] denotes greatest int function is?
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12 Answers
1dats correct.....cud u pls post the solution? Sorry if its too silly :(
11split the integral
by taking limits 0-1 and 1-2.....[x-1]-[x]
then you can do it
21by using the fact that {x} is a periodic functn ........ {x} = frac. part of x
I = [x] ∫a^tdt ................ the integral is over 0 to 1
10∫[x] at - [t] dt
= 0∫[x] a{t} dt .. now {.} is a periodic function with period 1
=[x] 0∫1 a{t} dt = [x] 0∫1 at dt
= [x] (a - 1)/ln a