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Math Help - how to find xi(bar) = .5(x(i-1) - xi) using the midpoint rule

  1. #1
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    how to find xi(bar) = .5(x(i-1) - xi) using the midpoint rule

    i need some help in finding xi using the midpoint rule. here is an example problem:

    integral from 0 to 1 of (1 + x^4)^(1/2) where n=10
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  2. #2
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    Quote Originally Posted by chse720 View Post
    i need some help in finding xi using the midpoint rule. here is an example problem:

    integral from 0 to 1 of (1 + x^4)^(1/2) where n=10
    As you are to use n=10 intervals they are each of length \delta x=[1-0]/10=0.1 and the mid points of the intervals are the points:

     <br />
x_i = (i-1) \delta x + \delta x/2=(i-1/2)\delta x, \ \ \ i=1, .. , 10 <br />

    and your integral:

     <br />
I \approx \delta x \left[ \sum_{i=1}^{10} (1 + x_i^4)^{1/2} \right]<br />

    .
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