## anonymous 5 years ago Determine the volume of the solid obtained by rotating the portion of the region bounded by and that lies in the first quadrant about the y-axis.

1. amistre64

your trying to tempt me arent ya :)

2. anonymous

Nope. Not in the least. ;)

3. amistre64

is this saying the volume of the first quadrant spun around the y axis?

4. anonymous

Yup. Which is to say, bound by both axis with the limits being each intersection

5. amistre64

i appear to be missing a function to determine proper bound lol; or have gone blind :)

6. anonymous

Oh you're right they didn't post... My bad! It's y=(x^1/3) and y =x/4

7. amistre64

x^3 = x/4 would be the bounds then right...

8. amistre64

cbrt(x)=x/4 typoed it lol

9. amistre64

im going with 0 to 4

10. amistre64

gotta redo that lol

11. amistre64

0 to 8 ...

12. anonymous

Yeah try again lol

13. anonymous

There you go

14. amistre64

my stupidity got in the way

15. anonymous

I forgive you. 64 is awfully close to one. ;)

16. amistre64

spin around the y axis....

17. amistre64

we can do this from 0 to 2 on the y right

18. anonymous

Less bored?

19. myininaya

lol nerds!

20. amistre64

less.... :)

21. anonymous

Yes, if you mean in terms of y.

22. amistre64

one radius is x=4y the other is .....

23. amistre64

y^3?

24. anonymous

I wouldn't do it that way.

25. amistre64

$\pi \int\limits_{0}^{2} [4y]^2 - [y^3]^2 dy$

26. anonymous

Though yes. You can. The top one being?

27. amistre64

why is it gonna break?

28. anonymous

Haha no,but yeah that's right. Let's pretend y just put inthe calculator and got it right because you can push buttons well. :)

29. amistre64

i get 128/3 - 128/7

30. amistre64

512/21 = 24.381 ??

31. amistre64

if I do shelss; i wonder if i get the same result :)

32. anonymous

That was fun :) it's 512 pi/21you forgot pi lol

33. amistre64

i think i dropped a pi lol

34. amistre64

ack!!.... yeah, just realized it :)

35. amistre64

76.59 closer?

36. amistre64

yes!! shell and disk are the same yay!!

37. amistre64

$2\pi \int\limits_{0}^{8} x(x^{4/3}) -x(\frac{x}{4}) dx$ = 76.59