# Definite integral using Riemann sums?

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

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lurflurf
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