The discussion focuses on approximating the integral of sin(sqrt(x)) from 0 to 40 using the midpoint rule with n=4. The user correctly calculates delta x as 10, creating four intervals: [0,10], [10,20], [20,30], and [30,40]. The midpoints for these intervals are identified as 5, 15, 25, and 35, which are the points where the function should be evaluated. The user struggles with the correct application of the midpoint formula and sigma notation, leading to incorrect results.
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skyturnred said:Homework Statement
I have to approximate the integral of sin(sqrt(x)) from 0 to 40, with n=4, using the midpoint rule.
Homework Equations
The Attempt at a Solution
I found delta x to be 10, obviously, since I have to approximate from 0 to 40 using 4 large rectangles. I am having trouble finding f(.5(x(of i-1)+x(of i)))). I don't really even know where to start!
LCKurtz said:Don't get lost in the subscripts. You have four intervals. What are their midpoints? Just list their x values. They are the four points where you evaluate the function.
skyturnred said:Ok, so I dropped the formula and just tried to think it through myself. It makes sense in my mind that the first midpoint is f(1/2), the next is f(3/2), then f(5/2), etc. So in terms of i in sigma notation (if i=0 and the upper limit is 40), it should be f(i+(1/2))(10), right? But somehow I am still getting the wrong answer..