## Unam 3 years ago Find the volume of the solid obtained by rotating the region bounded by x=8 y^2, y = 1, x = 0, about the y-axis. a) 8 y^2=0, x=0, how can I solve this when its like this, I mean there's no other x values so i can use the (0, ?)∫. I'm using this V = π ∫ f(x)² dx {a,b}

1. Unam

|dw:1351976086595:dw|

2. klimenkov

|dw:1351976458012:dw|

3. Unam

What's the graph between? 0 to 8 or 0 to 1?

4. klimenkov

You can't use this formula in this case.

5. Unam

oh ok...

6. klimenkov

|dw:1351976777364:dw| And now you can. Calculate this integral and it will be the volume.

7. Unam

thanks so down we... v= π (0,1) ∫(8x^2)^2 dx-(8-x)^2π?

8. Unam

don't*

9. klimenkov

Can't understand you, just calculate the integral I've written. And it will be the volume. Can you do this?

10. Unam

sorry, yup i can

11. klimenkov

You can type the result and I will check it.

12. Unam

ok :)

13. Unam

64π/5?

14. klimenkov

Yes. That's correct.

15. Unam

Oh thanks so much!

16. Unam

so I just use 1 and 0 for ∫?

17. Unam

|dw:1351977717019:dw|

18. Unam

i know how i get 0 but not sure about 1, we use the graph right? cos its not between 0 and 1?

19. klimenkov

You need to understand how the formula is built to get how to solve this problem. I just switch x and y, so you can use your formula.

20. Unam

Ah ok

21. klimenkov

If you will rotate the area on my second figure about x-axes you will get the volume i drew on the first figure. Got it?

22. Unam

YEs!!!

23. Unam

thanks much Klim!!

24. klimenkov

No problems.