# 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.

## Notes

• Add your names at the top of the document under the title.

## Submitting the Assignment

Once you are done with the assignment, share it with the instructor. Only one person per group needs to submit the assignment, just make sure your names are all in the document itself.

1. Click the blue "Share" button in Google Docs
2. In the "Invite People" box, put in james@richland.edu
3. Change the permissions from "Can edit" to "Can comment"
4. Leave the box checked to notify people via email (This is important or I won't know that you've turned it in).
5. Click on the "Add message" box and let me know what you're sending and the names of the people in your group.
6. Click "Send"