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  • <img alt="\int_{-2011}^{2011}\left \{ \left [ x^{2011} +x^{2009}+x^{2007}+x^{2005}+........+x\right ] \right \}dx \\ \\" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cint_%7B-2011%7D%5E%7

\int_{-2011}^{2011}\left \{ \left [ x^{2011} +x^{2009}+x^{2007}+x^{2005}+........+x\right ] \right \}dx \\ \\

                            +\int_{-2011}^{2011}\left \{ \left [ x^{2010} +x^{2008}+x^{2006}+........+1\right ] \right \}dx

is equal to (where \left [ . \right ]represents the greatest integer function and \left \{ . \right \} represents the fractional part function)

Option: 1

0
 


Option: 2

2\times \left ( 2011 \right )!


Option: 3

2^{2011}

 


Option: 4

2\times \left ( 2010 \right )!


Answers (1)

best_answer

Answer (1)

{[any real number]} = 0 and [{any real number}] = 0

So,

\int_{-2011}^{2011}\left \{ \left [ x^{2011} +x^{2009}+x^{2007}+x^{2005}+........+x\right ] \right \}dx \\ \\\; \; \; \;

                +\int_{-2011}^{2011}\left \{ \left [ x^{2010} +x^{2008}+x^{2006}+........+1\right ] \right \}dx=0

Posted by

manish painkra

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