8.1 Arc Length by SGLee - HSKim, JYLee, JHLee
1-6. Find the length of the curve.
1. 
, 
Since the length of the curve is 
,
=> 
. Substitute 
= a and 
.
So,
=> 
. 
=> 
.
Calculus-Sec-8-1-Solution
8.1 Arc Length by SGLee - HSKim, JYLee, JHLee
1-6. Find the length of the curve.
1. ,
Since the length of the curve is ,
=> . Substitute = a and .
So,
=> . => .
2. 
, 
.
3. 
, 
4. 
from 
to 
Since 
implies 
,
Let 
, then 
and 
.
, 
.
5. 
, 
, 
6. 
, 
Since 
,
.
8. 
, 
9. Find the length of the curve when 
goes to 0,
, 
.
http://matrix.skku.ac.kr/cal-lab/cal-8-1-11.html
11.(a) Graph the curve 
, 
.
(b) Compute the lengths of inscribed polygons with 
, 
, and 
sides.
(Divide the interval into equal subintervals.) Illustrate by sketching these polygons.
(c) Set up an integral to find the length of the curve.
(d) Use any of your CAS tool to find the length of the curve to four decimal places.
Compare with the approximations in part (b).
http://matrix.skku.ac.kr/cal-lab/cal-8-1-11-1.html
(a)
(b) 
(c) 
(d) Simpson's Rule with 
gives 
12. Repeat Exercise 11 for the curve 
, 
.
http://matrix.skku.ac.kr/cal-lab/cal-8-1-14.html
http://math1.skku.ac.kr/home/pub/1100/
(a)
(b) 
(c) 
(d) Simpson's Rule with 
gives 
.
7. Find the length of the curve as 
goes to 
.
, 
.
10. Find the length of the curve, 
, 
, 
.
