Wetzel

Math 140

4.2 – Area

Sigma Notation – Summation

                        =

            Ex.:

            1.) 

Area Under the Curve -        

            Graph the function, 

            The “Area Under the Curve” is the area between the curve and the x-axis.

            The Area Under the Curve of  is infinite since the function is continuous on the interval .

            However, the piece of the function from x = 1 to x = 2 does have a definite Area Under the Curve.  It has a starting point and an ending point.

 Finding the Area Under the Curve –

            Lower & Upper Sums –   Divide the area into rectangles and find the area of each rectangle.

                        1 Rectangle:

                        2 Rectangles:

                        4 Rectangles:

            Least amount of Error -