- #1
saxen
- 44
- 0
This shouldn't be a problem but I just can't this right!
Find the volume of the body that is generated when y= 1/x(sqrt(4-x^2)) ,1 <= x <2, is rotated around the y-axis
Using cylindrical shells :
2 pi ∫x (g(x)-f(x)) dx
2 pi ∫x (g(x)-f(x)) dx= 2 pi ∫1/sqrt(4-x^2) dx (Can I put f(x)=0?)
Using inverse substitution
x= 2sin t
dx= 2cos t dt
2 pi ∫dt
2 pi [t], Is it correct to use sin(2) and sin(1) as limits here?
Somewhere it all goes wrong, help is very much appreciated!
First post aswell, didn't find anywhere to introduce myself though. So hello all =)
Homework Statement
Find the volume of the body that is generated when y= 1/x(sqrt(4-x^2)) ,1 <= x <2, is rotated around the y-axis
Homework Equations
Using cylindrical shells :
2 pi ∫x (g(x)-f(x)) dx
The Attempt at a Solution
2 pi ∫x (g(x)-f(x)) dx= 2 pi ∫1/sqrt(4-x^2) dx (Can I put f(x)=0?)
Using inverse substitution
x= 2sin t
dx= 2cos t dt
2 pi ∫dt
2 pi [t], Is it correct to use sin(2) and sin(1) as limits here?
Somewhere it all goes wrong, help is very much appreciated!
First post aswell, didn't find anywhere to introduce myself though. So hello all =)