Section 5.6 – The Distance Formula and Method of Quadrature

In the coordinate plane, the distance d between two points and is given by the formula:

* You can also use the Pythagorean Theorem to find distance. Let a be the horizontal distance (run) and let b be the vertical distance (rise). Then, c would be the hypotenuse.

The Method of Quadrature

This is a method used to approximate the area of an enclosed region under a curve by using the sum of areas of a number of rectangles.

Left-hand Rule: use rectangles above the curve to approximate the area under the curve

Right-hand Rule: use rectangles below the curve to approximate the area under the curve.

Find the sum of the areas of all the rectangles from left-hand rule and the right-hand rule. Find the average of the two methods.