Problem

Approximate

with 4 trapezoids. Sketch a figure showing the curve and the trapezoids involved. Compare your answer with the answer you find using integration formulas.

Solution

Here's what the curve and the trapezoids look like.

Now we need to find the sum of the areas of the green, blue, brown, and magenta trapezoids. The easiest way to do this is to use the trapezoid rule formula for n = 4.

The y's are the y values of the function on the endpoints of the 4 intervals. We have

h, the width of each interval, is

Substitute these into the formula.

The answer using integration formulas is