Trapezoid+Rule

In calculus, the trapezoid rule is used to solve integrals just like Riemann sums are. Unlike Riemann sums, which uses rectangles to approximate the area under the curve, the trapezoid rule uses trapezoids. By using trapezoids instead of rectangles you get more of an accurate estimate of the area under the curve, the more trapezoids the more precise the estimate is. The only rule for the trapzoid rule is that all of the heights must be the same.

The equation for the trapzeoid rule is:

In this rule, the //h// stands for the height which would be the length on the x-axis, and the //b// stands for the second height of the trapezoid. The way you would draw the trapezoids is by drawing a straight line up the the line of the curve from the set interval and then connecting the lines from the straight line of the next set interval.

Example graph:

As you can see in this graph, all of the heights along the x-axis are equal (in this graph they are 1). The lines are drawn straight up to the line of the curve and meet the next straight line from the interval following it. The //b//'s would each be the value of the line up to the y-axis, and as shown in the rule you would continue to plug in the values for as many trapezoids there are in the graph.