Goal:to formulate, model and solve accurately problems involving estimating the area of a plane region using Riemann sums.

With the aid of the concepts about Riemann Sums,

- should be able to formulate an original problem which involves estimating the area under a curve by using Riemann Sum.

- document the step-by-step procedure.

-Take photo of your chosen parabolic object

What the need

• any object with parabolic surface/edge
• online graphing calculator

Guidelines

This involves one of the applications of Integration, which is finding/estimating the area under a curve using Riemann Sums. Follow these steps

1. Look for any parabolic object available in your homes, (the parabolic surface or edge will possibly be laid on a graphing paper later on). See the pictures below for some examples.

\fB. Using Desmos online graphing calculator In a graphing paper (or in an improvised grid on paper), construct a Cartesian plane focused on Quadrant 1, just like the one presented below. Trace a part of the parabolic surface or edge of the chosen object on the Cartesian plane available in your grid or graphing paper. You may opt to have the parabolic surface opening upward or downward. Take a photo of this since you will include it in your report. o Make sure that the parabola is well-graphed as you will use this in illustrating the area which you will estimate in the problem. o Identify three points from your graph. o Determine the equation of the parabola in the form y=ax2+bx+c using the three points from step (iii). If you cannot recall this process, you may watch a tutorial at this link: https://www.youtube.com/watch? v=ohc1futhFYM 3. Consider the identified equation of the parabola as a function which represents the graph of the parabolic curve and use this in the problem you will formulate. 4. Formulate word problem which involves finding or estimating the area between the graph of the parabolic function and the x-axis, using the Riemann Sum. Consider these additional conditions/instructions: Choose only (1) among the three types of Riemann sums: Right, Left or Midpoint. Mention this in your problem. Use at least 8 rectangles for the Riemann sum. Remember that the more rectangles you use, the more accurate the area will be. You decide on the interval that you will consider in finding the area. 5. Solve your own formulated problem, using the R-E-S-A format. Make sure to use the notations n, a, and b to represent the number of rectangles, lower and upper intervals, respectively, just like how we used it in our lecture on Riemann sums. Include the appropriate illustration (graph of the parabola from step 2), and table/'s needed in the solution. If there will be decimal numbers within the solution, as much as possible, use the exact value equivalent. If they happen to be continuous and non-terminating. you may round them off to 4 decimal places