## Dido525 Group Title Set up an intergal for the colume of the solid obtained by ratating the region bounded by the parabolas x=8y-2y^2, x= 4y-y^2 about the x-axis. one year ago one year ago

1. Dido525 Group Title

I have no idea how to do this :( .

2. tkhunny Group Title

The maximum x-value for each is at y = 2. The intersections of the two are at (0,0) and (0,4). Would you like to chop it up into 3 pieces or simply apply Pappus' Theorem?

3. Dido525 Group Title

I can't use Pappus' theorem.

4. tkhunny Group Title

Why not? Specifically proscribed? Not yet presented? Or just not able?

5. Dido525 Group Title

We won't learn it.

6. soty2013 Group Title

@saifoo.khan

7. Dido525 Group Title

First of all, I need to sketch this thing. I can't figure out how the thing looks like.

8. tkhunny Group Title

Think it up yourself and surprise everyone! 3 pieces then. 1) Biggest Piece x from 4 to 8 and y from $$2 - \sqrt{\dfrac{8-x}{2}}$$ to $$2 + \sqrt{\dfrac{8-x}{2}}$$ 2) Top Piece x from 0 to 4 and y from $$2 + \sqrt{4-x}$$ to $$2 + \sqrt{\dfrac{8-x}{2}}$$ 3) Bottom Piece x from 0 to 4 and y from $$2 - \sqrt{\dfrac{8-x}{2}}$$ to $$2 + \sqrt{4-x}$$ Go!

9. tkhunny Group Title

Why not flip it around to where you are more familiar and solve that problem. y = 8x-2x^2 and y= 4x-x^2 and wrap it around the y-axis!

10. Dido525 Group Title

But that changes the entire question.

11. tkhunny Group Title

No. The question is to calculate the volume. Unique answers do not care how you find them. It MUST be considered a valid methodology.

12. tkhunny Group Title

Anyway, you can flip it around just to get a look at it, if you can't relate to the present condition.

13. Dido525 Group Title

But if you switch the x and y's that should change the entire shape of the graph.

14. tkhunny Group Title

That's silly. Why would you think that? Absolutely not the case. It is the EXACT SAME problem.

15. Dido525 Group Title

|dw:1359609779642:dw| Something like that? REALLY bad sketch though.

16. tkhunny Group Title

|dw:1359609887178:dw| A little better. You crossed the x-axis. That's no good.

17. Dido525 Group Title

yeah I know. I felt lazy.

18. tkhunny Group Title

Well, go ahead and do it, then. I gave you all the limits up above. Good luck. gtg

19. Dido525 Group Title

Thanks!