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Ask iit jee aieee pet cbse icse state board experts Expert Question: DEFINITE integration 8
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kislay (1108)

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the value of ,0X [t+1]3dt   ([.] denotes greatest integer function)is equal to....


ans
([x]([x]+1)/2)2 + ([x]+1)3{x}


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sboosy (3046)

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integral
[t+1]cubed
=([t]+1)whole cubed using the fact that
[n+k]=[n]+k where k is a constant
so integral 0to x can be written as o to [x] and
[x] to x
first integral we get 1cube +2 cube+....[x] cubed
using formula it is first part of answer
next one
[x] to x the value of [x]+1 is constant
so that multipled with x-[x]={x}
so thats the answer
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elessar_iitkgp (2220)

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Well answered @sboosy



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kislay (1108)

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good answer sobsy...........

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