# Project 5: Integrals

## Instructions

Use Winplot, Google Docs, and possibly Microsoft Excel/Google Spreadsheets to create a document with two problems on it.

## Problem 1 - Approximating Areas

Consider the function $$y = 0.1 x^3 - \cos(x^2) - 0.5x + 2$$ on $$[-2,3]$$.

Use Winplot to create a graph of the curve on the interval. Include the graph in the document.

Use Winplot to complete this table.

Method 2 5 10 100 1000
Left endpoint
Midpoint
Right endpoint
Trapezoidal
Parabolic
Random

## Problem 2 - Web Pages

The instructor has a school website that receives thousands of hits each day. The hits column represents the number of hits (in thousands of hits per day) for that day.

 Date Hits Nov 1 Nov 5 Nov 8 Nov 17 Nov 18 Nov 21 Nov 30 43.398 71.863 43.841 60.835 77.347 70.385 36.982

Use the information to estimate the number of hits during the month of November 2013 using the five approaches given in the table. You may want to use a spreadsheet to speed up the calculations, although the data points are limited enough that you could do it by hand.

Method Estimate Relative Error
Left endpoints
Right endpoints
Trapezoids
Minimums
Maximums

The total count for the month was 1714.325 thousand hits (1.714 million). The relative error is usually given as a percent. You take the estimate minus the actual value and then divide by the actual value. Finally, convert that into a percent.

## Additional Notes

• Add your names at the top of the document under the title.
• To submit the assignment, click the Share button in Google Docs and change it so that anyone with the link can view the results. Then copy the share link and email it to the instructor at james@richland.edu with an appropriate subject and the names of the people in the group. Only one person per group needs to submit the project.

## Winplot Tips

### Equa Menu

• Use implicit to graph an implicit equation. Sometimes, implicit graphs have a problem displaying if you change the zoom or arrow around to change the viewing. A workaround is to edit the graph in the inventory and then change the color.
• The inventory has a derive button that will graph the derivative of the selected function. The graph button will show or hide a graph, so a good way to make matching graphs is to sketch the function and derivative to make sure both are going to fit reasonably well on in the viewing window and then show one while hiding the other when you copy and paste the graph.

### One Menu

• Use Measurement / Integrate to determine the areas. After setting it up, click on Definite to obtain the estimates.