Illustrate then answer the following questions.

Question

Procedure:

1. Draw a Cartesian plane on a ¼ size illustration board (use a scale of 1 centimeter.

2. Plot the graph of the parabola (x – 1)2 = – 16(y – 4) on the Cartesian plane. (Note that the

parabola is opening downward)

3. Divide the bounded region between the graph and the x-axis into approximately 8 equal parts.

4. Cut a rectangular strip (use bond paper or colored paper) that will exactly fit each part of the

bounded region.

5. Paste the strip on the graph from the left x-intercept all through out to the right x-intercept. Make

sure the middle top of the strip intersects the parabola.

6. After the entire region is covered by the strips, calculate the area of each rectangular strip and

write it on top.

7. You are now ready to perform the task below.

Reiman sums approximate area under a curve by accumulating the areas of rectangles. On a piece of

paper,

a. Compute the approximate area of the region bounded by the parabola and the x-axis.

b. Describe the application of the Reiman sums?

(Note: If you don't have the materials, then just draw something to represent it.Thank you.)

Answer 1

Obviously I'm not going to be able to help you with this whole question but suffice it to say that the results of questions 1 - 5 will look like this:

The area is just the width of each box times the height (which you can measure - make sure to account for your scale).

The Reimann sums can be left, right, or midpoint. To do the left, make boxes that align with the function graph at the left side of the box. To do the right, make boxes that align with the function graph at the right side of the box. The midpoint will look like the boxes in the figure above.