How do I use the midpoint rule to approx integral sin(sqrt(x)) from 0 to 40

[skyturnred]

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]

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!

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]

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.

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..

 

[LCKurtz]

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..

If you have 4 equal intervals on [0,40] your partition points presumably are 0,10,20,30,40. Do you think 1/2 is the mid point of [0,10]? And you don't have a sum up to 40, there are only 4 intervals.