# I need some intuition

1. Jul 10, 2014

### MMM

1. The problem statement, all variables and given/known data
I'm curious about how the trapezoidal rule is derived for approximating definite integrals.

2. Relevant equations

According to my calculus book the equation is $$h[(1/2)y_{0} + y_{1} + y_{2} + ... +y_{n-1} + (1/2)y_{n}]$$

3. The attempt at a solution
I'm curious as to why the first and last y values are multiplied by $$1/2$$
I've solved a lot of problems using the trapezoidal rule, but I don't quite understand it. Any insight on why the first and last y values are multiplied by $$1/2$$.

2. Jul 10, 2014

### Staff: Mentor

You are representing the area under the curve as a set of trapezoids. The total area is h(y0 + y1)/2 + h(y1 + y2)/2 ... and so on. The 1/2 goes away for all points but the first and last.

3. Jul 10, 2014

### MMM

I get it now, I appreciate the help.