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Homework Help: Definite integral using Riemann sums?

  1. Nov 11, 2011 #1
    I'm reviewing my Calc 1 material for better understanding. So, I was reading about the area under a curve and approximating it using Riemann sums. Now, I understand the method, but I was a little confused by finding xi*. I know there is a formula for it xi*=a+Δx(i). What does the "i" stand for?

    I was looking at a problem for f(x)=cos(x) and its bounded by x=0 and x=∏/2, with four subintervals. Also, the problem states to use the xi sample points as the midpoints. I understand how to do it, but I don't get what the "i" represents.

    If this helps x1*=∏/16, x2*=3∏/16, x3*=5∏/16, and x4*=7∏/16

    Thanks
     
  2. jcsd
  3. Nov 11, 2011 #2

    lurflurf

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    Homework Helper

    i is just the number of the interval
    x1*=∏/16, x2*=3∏/16, x3*=5∏/16, and x4*=7∏/16
    could be written
    xi*=(∏/16)(2i-1)
    for i=1,2,3,4
     
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