Download presentation

Presentation is loading. Please wait.

Published byLindsey Budd Modified about 1 year ago

1
Applications of Integration Volumes of Revolution Many thanks to http://mathdemos.gcsu.edu/shellmeth od/gallery/gallery.html

2
Method of discs

3
Take this ordinary line 2 5 Revolve this line around the x axis We form a cylinder of volume

4
We could find the volume by finding the volume of small disc sections 2 5

5
If we stack all these slices… We can sum all the volumes to get the total volume

6
To find the volume of a cucumber… we could slice the cucumber into discs and find the volume of each disc.

7
The volume of one section: Volume of one slice =

8
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

9
The volume of one section: r = y value h = dx Volume of one slice =

10
Volume of cucumber… Area of 1 slice Thickness of slice

11
Take this function… and revolve it around the x axis

12
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=

13
Take this shape…

14
Revolve it…

15
Christmas bell…

16
Divide the region into strips

17
Form a cylindrical slice

18
Repeat the procedure for each strip

19
To generate this solid

27
A polynomial

30
Regions that can be revolved using disc method

31
Regions that cannot….

32
Model this muffin.

33
Washer Method

34
A different cake

35
Slicing….

36
Making a washer

38
Revolving around the x axis

39
Region bounded between y = 1, x = 0, y = 1 x = 0

40
Volume generated between two curves y= 1

41
Area of cross section.. f(x) g(x)

42
dx

43
Your turn: Region bounded between x = 0, y = x,

44
Region bounded between y =1, x = 1

48
Region bounded between

49
Around the x axis- set it up

50
Revolving shapes around the y axis

51
Region bounded between

53
Volume of one washer is

54
Calculate the volume of one washer

55
And again…region bounded between y=sin(x), y = 0.

57
Region bounded between x = 0, y = 0, x = 1,

59
Worksheet 5 Delta Exercise 16.5

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google