Illustrate then do the following :a. Compute the approximate area of the region bounded by the parabola and the x-axis. b. Describe the application of the Reiman sums?

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?

Answer 1

I used a left Riemann sum here, but you can use a Midpoint and Right Riemann sum. Below is the link to an image of the graph.

https://ibb.co/w66F0xT