∫ 2 x-[x] .dx limits from 0 to [x]

2x-[x]  .dx

limits from 0 to [x]


1 Answers

bibhash jha
15 Points
13 years ago


To solve this divide the integrals into o to 1 ,1 1to 2 ..... upto [x]-1 to [x]


so you get integrations of 2^(x-0) from 0 to 1 +2^(x-1) from 1 to 2 .... upto 2^(x-[x]+1) from [x-1]to [x]


each integral evaluates to 1/ln2 so we have [x] terms in our integral sum expression ..


therefore you get  ans=[x]/ln2

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