How to Apply the Composite Trapezoidal Rule When Integrating y dx?

[VooDoo]

Hey guys,

Im a bit baffled on this one.

I have been told to perform the following integration:
\int y dx from -1 to 14. I have been given some values of x and the corresponding values of y.

I just have one question, the fact that it is y dx is throwing me off. The trapazoidal rule is: I = h* [f(x1)-f(x2)]/2. This is probably really simple and a dumb question, but I assume that f(x1) corresponds to the value of y that I have been given for x1?

 

[HallsofIvy]

Yes, that is what the standard notation y= f(x) means. Now I notice that you title this "composite" trapezoidal rule. The trapezoidal rule you give is for just two points: one trapezoid. If you are given a number of x and y values, you will want to do a different trapezoid for each pair of points, the "right" side of one trapezoid being the "left" side of the other. If, for example, you had 3 points (x₁,y₁), (x₂,y₂),(x₃,y₃), then the "trapezoid" between x₁ and x₂ has area (y₂- y₁)/2(x₂-x₁) and the "trapezoid" between x₂ and x₃ has area (y₃- y₂)/2(x₃-x₂). The total area, of course, would be the sum of those.

 

[tiny-tim]

I just have one question, the fact that it is y dx is throwing me off. The trapazoidal rule is: I = h* [f(x1)-f(x2)]/2. This is probably really simple and a dumb question, but I assume that f(x1) corresponds to the value of y that I have been given for x1?

Hi VooDoo!

Yes, y is a function of x, just like any old f, but we don't normally write y(x), so you have to imagine the "(x)"

So f(x1) = y(x1) = the value of y at x = x1.