Area between two curves
Download
1 / 9

Area Between Two Curves - PowerPoint PPT Presentation


  • 57 Views
  • Uploaded on

Area Between Two Curves. Math 5A. The Problem. Find the volume of the solid formed when the region bounded by y=sqrt(x) , x=4 and the x axis is revolved about the x axis. The Idea Behind the Solution. Suppose we tried slicing this solid into 4 pieces by slicing perpendicular to the x axis.

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 ' Area Between Two Curves' - laith-lopez


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

The problem
The Problem

  • Find the volume of the solid formed when the region bounded by y=sqrt(x) , x=4 and the x axis is revolved about the x axis.


The idea behind the solution
The Idea Behind the Solution

Suppose we tried slicing this solid into 4 pieces by slicing perpendicular to the x axis.

Those four slices would look approximately like the four circular disks shown at the right, only the outer surface would not be as straight. We can approximate the volume of the solid by computing the volume of these four disks.


Finding the volume of the disks
Finding the Volume of the Disks

The volume of each disk is pr2h where h is the thickness of each disk

(1 in this case, in general) and r is the functional value at a a point in the subinterval.


Volume for 4 disks
Volume for 4 disks

Approximation using 4 disks. For a better approximation, use more disks.





The disk method just add up the
The Disk Method – Just add up the

For a solid formed by revolving a region bounded above by f(x) on [a,b] about the x axis…


ad