arc length and surface area
Download
Skip this Video
Download Presentation
Arc Length and Surface Area

Loading in 2 Seconds...

play fullscreen
1 / 20

Arc Length and Surface Area - PowerPoint PPT Presentation


  • 110 Views
  • Uploaded on

Arc Length and Surface Area. Compiled by Mrs. King. Start 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/.../ arc hives/ arclength / arclength . ppt. The Length of a Polygonal Path?.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Arc Length and Surface Area' - sophia-rosales


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
arc length and surface area

Arc Length and Surface Area

Compiled by Mrs. King

start with something easy
Start with something easy

The length of the line segment joining points (x0,y0) and (x1,y1) is

(x1,y1)

(x0,y0)

www.spsu.edu/math/Dillon/2254/.../archives/arclength/arclength.ppt

the length of a polygonal path
The Length of a Polygonal Path?

Add the lengths of the line segments.

www.spsu.edu/math/Dillon/2254/.../archives/arclength/arclength.ppt

the length of a curve
The 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

approximate the curve with polygonal pieces
Approximate the curve with polygonal pieces?

www.spsu.edu/math/Dillon/2254/.../archives/arclength/arclength.ppt

what are we doing
What 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.
arc length
Arc Length
  • 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

example problem
Example Problem
  • Compute the arc length of the graph of over [0,1].
now comes the fun part
Now 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!
example
Example
  • 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

you try
You 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

surface area

Surface Area

Compiled by Mrs. King

review
Review:
  • 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.dreamhosters.com/2/2d/Basic_cubic_function_graph.gif

surface area of solids of revolution
Surface Area of Solids of Revolution
  • 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

what are we doing1
What 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
ex 2 5
Ex 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

closure
Closure
  • 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

homework
Homework
  • Page
  • #
ad