Is the Midpoint Rule Different from Simpson's Rule?

[kait]

Homework Statement

I'm working on a practice test and got stuck on the question: Approximate the length of the curve y=√x, 0≤x≤1 by the midpoint rule with n=4 and ∆x=0.25.

Homework Equations

Is the midpoint rule the same thing as Simpson's rule? I don't remember going over the midpoint rule in class and I can't find it in the book. If it isn't the same as Simpson's rule, what is it?

 

[Mark44]

I would guess that in finding the length of a curve by the midpoint rule, you calculate the function value at the midpoint of each subinterval, and then calculate the lengths of those line segments that join those points. For the approximate arc length, just add those lengths together.

 

[HallsofIvy]

No, the midpoint rule is not the same as Simpson's rule. With Simpson's rule, you approximate the curve by a series of parabolas through each set of 3 points.

As Mark44 says, the midpoint rule uses the midpoint of each interval to compute the height of a rectangle on that interval.