Download presentation

Presentation is loading. Please wait.

Published byDeshaun Doolittle Modified over 3 years ago

2
A RC L ENGTH AND S URFACE A REA Compiled by Mrs. King

3
S TART WITH SOMETHING EASY The length of the line segment joining points (x 0,y 0 ) and (x 1,y 1 ) is (x 1,y 1 ) (x 0,y 0 ) www.spsu.edu/math/Dillon/2254/.../archives/arclength/arclength.ppt

4
T HE L ENGTH OF A P OLYGONAL P ATH ? Add the lengths of the line segments. www.spsu.edu/math/Dillon/2254/.../archives/arclength/arclength.ppt

5
T HE LENGTH OF A CURVE ? Approximate by chopping it into polygonal pieces and adding up the lengths of the pieces www.spsu.edu/math/Dillon/2254/.../archives/arclength/arclength.ppt

6
A PPROXIMATE THE CURVE WITH POLYGONAL PIECES ? www.spsu.edu/math/Dillon/2254/.../archives/arclength/arclength.ppt

7
W HAT ARE WE DOING ? In essence, we are subdividing an arc into infinitely many line segments and calculating the sum of the lengths of these line segments. For a demonstration, let’s visit the web.web

8
T HE F ORMULA :

9
A RC L ENGTH Note: Many of these integrals cannot be evaluated with techniques we know. We should use a calculator to find these integrals. phs.prs.k12.nj.us/preyes/Calculus%205-4.ppt

10
E XAMPLE P ROBLEM Compute the arc length of the graph of over [0,1].

11
N OW COMES THE FUN PART … First, press the Math button and select choice 9:fnInt( Next, type the function, followed by X, the lower bound, and the upper bound. Press Enter and you get the decimal approximation of the integral!

12
E XAMPLE Find the arc length of the portion of the curve on the interval [0,1] phs.prs.k12.nj.us/preyes/Calculus%205-4.ppt

13
Y OU TRY Find the arc length of the portion of the curve on the interval [0,1] phs.prs.k12.nj.us/preyes/Calculus%205-4.ppt

14
S URFACE A REA Compiled by Mrs. King

15
R EVIEW : Find the volume of the solid created by rotating about the x-axis on the interval [0,2] Picture from: http://math12.vln.dreamhosters.com/images/math12.vln.dream hosters.com/2/2d/Basic_cubic_function_graph.gif

16
S URFACE A REA OF S OLIDS OF R EVOLUTION When we talk about the surface area of a solid of revolution, these solids only consist of what is being revolved. For example, if the solid was a can of soup, the surface area would only include the soup can label (not the top or bottom of the can) phs.prs.k12.nj.us/preyes/Calculus%205-4.ppt

17
W HAT ARE WE DOING ? Instead of calculating the volume of the rotated surface, we are now going to calculate the surface area of the solid of revolution

18
T HE F ORMULA :

19
E X 2.5 Find the surface area of the surface generated by revolving about the x-axis phs.prs.k12.nj.us/preyes/Calculus%205-4.ppt

20
C LOSURE Hand in: Find the surface area of the solid created by revolving about the x- axis phs.prs.k12.nj.us/preyes/Calculus%205-4.ppt

21
H OMEWORK Page #

Similar presentations

OK

Arc Length Cartesian, Parametric, and Polar. Arc Length x k-1 xkxk Green line = If we do this over and over from every x k—1 to any x k, we get.

Arc Length Cartesian, Parametric, and Polar. Arc Length x k-1 xkxk Green line = If we do this over and over from every x k—1 to any x k, we get.

© 2018 SlidePlayer.com Inc.

All rights reserved.

By using this website, you agree with our use of **cookies** to functioning of the site. More info in our Privacy Policy and Google Privacy & Terms.

Ads by Google

Ppt on google glasses technology Ppt on sources of energy for class 8th examination Pdf to ppt online converter free download Ppt on acid-base titration formula Ppt on any one mathematician john Ppt on autotrophic mode of nutrition Ppt on power grid corporation of india limited Ppt on marketing management by philip kotler videos Ppt on stock exchanges in india Ppt on technology development in india