## anonymous 3 years ago Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=1/x^4, y=0, x=2, x=6, about y=-4

1. anonymous

I would use the method of cylindrical shells. At any f(x) value between 2 and 6, what is the radius from that y point to y = -4?

2. anonymous

Which method u prefer? shell or washer?

3. anonymous

I just need help setting it up to integrate then i can take it from there...

4. anonymous

The setup of the integral depends on the method you use....

5. anonymous

^ I didn't see your comment.. the washer method :)

6. anonymous

7. anonymous

isn't easier? or not? usually for me it is easier..

8. anonymous

i agree that washer is appropriate here.... hang on....

9. anonymous

You guys have fun with that >_>

10. anonymous

|dw:1361159214153:dw|

11. anonymous

Can you give me the expression for R and r?

12. anonymous

errr.. ;/ crap.

13. anonymous

???

14. anonymous

no... i don't think it's that.. :)

15. anonymous

haha give me a sec

16. anonymous

consider this...|dw:1361159501396:dw|

17. anonymous

would it be 1/x^4-4

18. anonymous

squared

19. anonymous

for R, shouldn't it be 1/x^4 + 4 ???

20. anonymous

- - + .. err yeah my bad

21. anonymous

ok... you also agree that r = 4 (inner radius) ???

22. anonymous

yupp it is

23. anonymous

so... $$\large dV=\pi(R^2-r^2)dx$$ so $$\large V=\pi \int_2^6(R^2-r^2)dx$$ you replace the expressions for R and r ....

24. anonymous

sorry... i gotta leave... :(

25. anonymous

i'm pretty sure what we have is correct....