• Support PF! Buy your school textbooks, materials and every day products Here!

Integration problem

  • Thread starter andrew.c
  • Start date
  • #1
46
0

Homework Statement



A solid rotor ring is made by rotation round the x-axis the area enclosed between the lines y=x+5 and y=2x+7 between the x-values x=0 and x=1.
Find its volume.

Homework Equations


n/a


The Attempt at a Solution


[tex]ytobeintegrated = 2x+7-x-5 \\= x+2\\\int (x=2)dx \\=\left[\frac{x^2}{2}+2x\right](between 1 and 0) \\=3.5 units[/tex]

What next? I think this is only giving me the area in one plane? Do i just multiply by 360 degrees?
 

Answers and Replies

  • #2
1,100
0
You cannot simply take away the two functions before integration or multiply by 360 degrees. Also, if you integrate any 2-dimensional, cartesian function without any manipulation you will only get the area under that function. So although your integration is correct (though your solution should be 2.5 cubic units not 3.5), the idea is not.

Try using:

[tex]Volume \ = \ \int_{a}^{b} \pi f(x)^{2} \ dx[/tex]
where f(x) is one of the functions.

What do you think is the next step?

The Bob
 
Last edited:

Related Threads on Integration problem

  • Last Post
Replies
8
Views
1K
Replies
4
Views
2K
Replies
8
Views
1K
  • Last Post
Replies
11
Views
933
  • Last Post
Replies
6
Views
882
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
7
Views
740
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
1K
Top