# Composite Trapezoidal Rule Help

1. Aug 20, 2008

### 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?

2. Aug 20, 2008

### 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.

3. Aug 20, 2008

### tiny-tim

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.