## agentx5 Group Title Is this setup correct? Q: "Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis." x = 1 + y$$^2$$, x = 0, y = 1, y = 3 $\huge\int\limits_0^{\sqrt{2}} (2 \pi)(y)((3) - (1+y^2)) dy$ y=3 is the right function x=1+y$$^2$$ is the left function right - left Graph below: 2 years ago 2 years ago

1. agentx5 Group Title

|dw:1341360986379:dw| Look good @KingGeorge ? :-)

2. KingGeorge Group Title

I think you switched some things around. First of all, the lines you drew for y=1,3 are vertical lines when they should be horizontal. In short, check the area you want integrate again.

3. agentx5 Group Title

Wait a minute I'm getting zero when I evaluate...

4. agentx5 Group Title

Oh... I think believe I see what I did there, let's try that graph again: |dw:1341361482202:dw|

5. KingGeorge Group Title

That looks better. So your new integrand and bounds would be...?

6. agentx5 Group Title

$\huge\int\limits_1^3 (2 \pi)(y)((3) - (1+y^2)) dy = -\frac{26}{3}$ The shells are growing out from the x-axis but I'm still missing something, a radius change perhaps? But which one? +1 or -1?

7. agentx5 Group Title

Seems like 1-y is logical for a shift upward, the others evaluate negative

8. KingGeorge Group Title

The only change I would make is in the integrand again. The right side is now $$(1+y)^2$$ and the left is 0. Hence, you should have $\huge\int\limits_1^3 (2 \pi)(y)( (1+y^2)-0) dy$

9. agentx5 Group Title

$\large \int\limits_1^3 (2 \pi)(y)( (1+y^2)-0) dy =^? \int\limits_1^3 (2 \pi)(1-y)((3) - (1+y^2)) dy = \frac{44}{3}$

10. agentx5 Group Title

No wait the first is 44/3 and the second is 44$$\pi$$/3

11. KingGeorge Group Title

I think I forgot a close parentheses. $\huge\int\limits_1^3 (2 \pi)(y)( (1+y)^2) dy$

12. agentx5 Group Title

Just noticed it ran off the page too, sry about breaking margins >_<

13. agentx5 Group Title

$\huge\int\limits_1^3 (2π)(y)((1+y)^2)dy = \frac{248\pi }{3}$ Seems logical, let me give it a try...

14. agentx5 Group Title

Alas no, it is incorrect

15. agentx5 Group Title

Sheesh these particular problems are being, well, problems tonight :D

16. agentx5 Group Title

*looks back over steps*

17. KingGeorge Group Title

Wait, I misread the question. There shouldn't be a close parentheses there XD Have you already tried it without the close parentheses that I added?

18. agentx5 Group Title

(2π)(y)((1+y)^2)dy <-- literally what I started working with

19. agentx5 Group Title

Oh it's on the wrong side!

20. KingGeorge Group Title

How about $\large\int\limits_1^3 (2 \pi)(y)( 1+y^2) dy?$

21. agentx5 Group Title

That's a quadratic now by mistake

22. agentx5 Group Title

And 48π is perfectly correct, awesome!!!

23. agentx5 Group Title

Comes out very nice in the end, no fractions

24. KingGeorge Group Title

Awesome. Now I just need to read the problems correctly.

25. agentx5 Group Title

Me too lol

26. agentx5 Group Title

What am I thinking, making vertical lines when it asked for horizontal lol