The graph of the function f left parenthesis x right parenthesis equals StartRoot 4 minus x squared EndRoot

f(x)=

4x2 on the interval negative 2 less than or equals x less than or equals 2

2x2 is a semicircle. The area under the graph is one half pi left parenthesis 2 right parenthesis squared almost equals 6.28319 comma

12(2)26.28319, to five decimal places. Use a Riemann sum with n equals 5

n=5 and midpoints to estimate the area under the graph. Then compute the error(the difference between the estimate and 6.28319

6.28319).

A coordinate system has a horizontal x-axis with tick marks at negative 2, 0 and 2 and a vertical y-axis with a tick mark at 2. From left to right, a curve labeled y equals StartRoot 4 minus x squared EndRoot starts at (negative 2, 0), rises to a maximum at (0, 2), and falls to (2, 0). Five rectangles of equal width are drawn under the curve so that there is no space in between them. Vertical dashed line segments extend from the top midpoint of each rectangle to the x-axis. The top midpoint of each rectangle is a point on the curve.

y equals StartRoot 4 minus x squared EndRoot

y=

4x2

2

-2

2

0

x