The discussion revolves around approximating the integral of sin(sqrt(x)) from 0 to 40 using the midpoint rule with n=4. Participants are exploring the setup and calculations involved in applying this numerical method.
The discussion is ongoing, with participants providing guidance on identifying midpoints and questioning the original poster's understanding of the intervals and calculations. There is a focus on clarifying the setup rather than reaching a conclusion.
Participants note that the original poster has calculated delta x as 10 and are discussing the implications of this choice on the midpoints and function evaluations. There is an emphasis on correctly interpreting the intervals and midpoints in the context of the problem.
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..