Problem 3E

Explain geometrically how the Trapezoid Rule is used to approximate a definite integral.

Solution:-

Step1

Trapezoid Rule - We can approximate the exact area under a curve between a and b,

Where n is the number of trapezoids equals a, and through are the equally spaced x coordinates of the right edges of trapezoids 1 through n.

Step2

Example

The figure below shows three trapezoids drawn under the function

For the function in the above figure with three trapezoids, here’s the math

=

=

=

=

=13.5