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Math Help - Use upper and lower sum to show that

  1. #1
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    Use upper and lower sum to show that

    0.6 < \int _0\,^1\!dx/(1+x^2) <1

    I am not sure what the partition is, to find the upper and lower sum, we need the partition and sub interval to do it. Can someone clear it ?
    Last edited by 450081592; January 12th 2010 at 05:02 PM.
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  2. #2
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     0.6< \int_0^1\frac{dx}{1+x^2} <1 \implies 0.6<\tan^{-1}x+c <1
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    Quote Originally Posted by pickslides View Post
     0.6< \int_0^1\frac{dx}{1+x^2} <1 \implies 0.6<\tan^{-1}x+c <1

    What! where is the tan from? Don't we need to find the lower sum and upper sum?
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  4. #4
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    Quote Originally Posted by 450081592 View Post
    What! where is the tan from?
     <br />
\int_0^1\frac{dx}{1+x^2} =\left[\tan^{-1}x \right]_0^1<br /> <br />

    Just thought it would come in helpful.
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  5. #5
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    Quote Originally Posted by pickslides View Post
     <br />
\int_0^1\frac{dx}{1+x^2} =\left[\tan^{-1}x \right]_0^1<br /> <br />

    Just thought it would come in helpful.

    I still don't understand where tan come from? which one is the lower sum and upper sum? We havent covered how to find the integration of a function, Is the first time I deal with interation, so can you explain more thanks
    Last edited by 450081592; January 12th 2010 at 06:08 PM.
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