We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byLindsey Budd
Modified over 2 years ago
Applications of Integration Volumes of Revolution Many thanks to http://mathdemos.gcsu.edu/shellmeth od/gallery/gallery.html
Method of discs
Take this ordinary line 2 5 Revolve this line around the x axis We form a cylinder of volume
We could find the volume by finding the volume of small disc sections 2 5
If we stack all these slices… We can sum all the volumes to get the total volume
To find the volume of a cucumber… we could slice the cucumber into discs and find the volume of each disc.
The volume of one section: Volume of one slice =
We could model the cucumber with a mathematical curve and revolve this curve around the x axis… Each slice would have a thickness dx and height y. 25 -5
The volume of one section: r = y value h = dx Volume of one slice =
Volume of cucumber… Area of 1 slice Thickness of slice
Take this function… and revolve it around the x axis
We can slice it up, find the volume of each disc and sum the discs to find the volume….. Radius = y Area = Thickness of slice = dx Volume of one slice=
Take this shape…
Divide the region into strips
Form a cylindrical slice
Repeat the procedure for each strip
To generate this solid
Regions that can be revolved using disc method
Regions that cannot….
Model this muffin.
A different cake
Making a washer
Revolving around the x axis
Region bounded between y = 1, x = 0, y = 1 x = 0
Volume generated between two curves y= 1
Area of cross section.. f(x) g(x)
Your turn: Region bounded between x = 0, y = x,
Region bounded between y =1, x = 1
Region bounded between
Around the x axis- set it up
Revolving shapes around the y axis
Region bounded between
Volume of one washer is
Calculate the volume of one washer
And again…region bounded between y=sin(x), y = 0.
Region bounded between x = 0, y = 0, x = 1,
Worksheet 5 Delta Exercise 16.5
Volume: The Shell Method Lesson 7.3. Find the volume generated when this shape is revolved about the y axis. We can’t solve for x, so we can’t use a horizontal.
6.3 Volumes by Cylindrical Shells. Find the volume of the solid obtained by rotating the region bounded,, and about the y -axis. We can use the washer.
Volumes of Revolution Disks and Washers
Volume: The Disk Method
Chapter 5: Integration and Its Applications
Volumes Lesson 6.2.
Volumes by Cylindrical Shells. What is the volume of and y=0 revolved around about the y-axis ? - since its revolving about the y-axis, the equation needs.
Volume. Find the volume of the solid formed by revolving the region bounded by the graphs y = x 3 + x + 1, y = 1, and x = 1 about the line x = 2.
Volumes of Revolution The Shell Method Lesson 7.3.
Volumes – The Disk Method Lesson 7.2. Revolving a Function Consider a function f(x) on the interval [a, b] Now consider revolving that segment of curve.
Section 7.2 Solids of Revolution. 1 st Day Solids with Known Cross Sections.
7.1 Areas Between Curves To find the area: divide the area into n strips of equal width approximate the ith strip by a rectangle with base Δx and height.
Solids of Revolution Revolution about x-axis. What is a Solid of Revolution? Consider the area under the graph of from x = 0 to x = 2.
Volumes of Solids of Rotation: The Disc Method
Solids of Revolution Washer Method
Review: Volumes of Revolution. x y A 45 o wedge is cut from a cylinder of radius 3 as shown. Find the volume of the wedge. You could slice this wedge.
Volumes by Slicing. disk Find the Volume of revolution using the disk method washer Find the volume of revolution using the washer method shell Find the.
Disks, Washers and Shells Limerick Nuclear Generating Station, Pottstown, Pennsylvania.
TOPIC APPLICATIONS VOLUME BY INTEGRATION. define what a solid of revolution is decide which method will best determine the volume of the solid apply the.
© 2017 SlidePlayer.com Inc. All rights reserved.