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mathGiven I = Integral x^n/(x+1) demonstrate that I <= 1/(n+1). The limits of...

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userwtf | eNotes Newbie

Posted February 4, 2013 at 9:41 AM via web

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Given I = Integral x^n/(x+1) demonstrate that I <= 1/(n+1). The limits of integration are x=0 to x=1 and n is natural number.?????

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userwtf | eNotes Newbie

Posted February 4, 2013 at 9:42 AM (Answer #2)

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Given I = Integral x^n/(x+1) demonstrate that I <= 1/(n+1). The limits of integration are x=0 to x=1 and n is natural number.

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted February 4, 2013 at 9:57 PM (Answer #3)

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`int_0^1 x^n/(n+1)=x^(n+1)/(n+1)^2|_0^1=1/(n+1)^2`

So your integral is equal to `1/(n+1)^2` which is less than `1/(n+1)` because n is a natural number.

I'm sorry because the above formula is hard to read. You should've posted this as a question under math.

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