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Approximating this integral with midpoints

  1. Nov 20, 2014 #1
    I have an integral from 0 to 1, of sin(x2).
    I need to, with n=5 rectangles midpoint approximate it.

    I've figured that I need something like i=1 and ending at 5 (right?), and the equation is just sin(x2) Δx
    Delta x is 1/5.

    Are those the correct steps?
    I think that all I need to do....
    is... uhh.......... Well, actually I'm not sure how to change x2. Should it be xi2?

    If that's true, then I think all I need to do, to midpoint approxy is keep on incrementing i, and I think it naturally gives me a midpoint, right?
  2. jcsd
  3. Nov 20, 2014 #2


    Staff: Mentor

    Yes, you need to have an x value (xi) for each subinterval. If xi - 1 and xi are then endpoints of a given subinterval you need to evaluate your function f at ##\frac{x_{i - 1} + x_i}{2}##, the midpoint of that subinterval.
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