Purpose: The purpose of this project is three-fold Apply the calculus procedure

Question

Purpose: The purpose of this project is three-fold Apply the calculus procedure of finding arc length to a real situation Learn how to fit an nth degree least squares (regression) polynomial function to a set of data Use technology to estimate the value of a definite integral that may be too difficult to compute using calculus alone. The Problem: have cut a pice of wire to a pre-determined length. gave it some bends, and photocopied it with a piece of centimeter graph paper as a background. Your job is to find out how many centimeters long the wire was when Ifirst cut it off the spool and measured it with a ruler. How You Will Be Graded: Each part of this investigation is worth a certain number of points. When grading each section I will be evaluating: The correctness of your math The organization and clarity of your work Whether you followed directions and answered all questions Unless directed otherwise do your work and write your responses on a separate piecels) of paper. Procedure: Step on the graph paper (with the outline of the wire), label the units or the x- and y-axes. Each block on the paper is 1 cm in width. Step 2 On the graph, choose 11 points that you will use to build your polynomial function. They do not have to be equally spaced apart. Make sure you choose the two endpoints as well as any critical points (maxs or mins), inflection points, and any other points you feel are important. Make sure you have exactly 11 points. On a separate sheet of paper, write the sub-heading "Step 2", and list the coordinates of your 11 points.

Explanation / Answer

Choose the bottom left point as origin and follow convention

Im choosing the following 10 points

0,11
1,7
3,5
5,4
7,7
9,9
10,9
11,8
12,6
13,5
16,4

Now the respective distance will be

Similarly we can go on to carry on all distance and sum them up

sqrt{17}+2sqrt{2}+sqrt{5}+sqrt{13}+2sqrt{2}+1+sqrt{2}+sqrt{5}+sqrt{2}+sqrt{10}

= sqrt{17}+2sqrt{2}+sqrt{5}+sqrt{13}+2sqrt{2}+1+sqrt{2}+sqrt{5}+sqrt{2}+sqrt{10}

= 24.84 cm

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