## monroe17 Group Title Find the volume formed by rotating the region enclosed by: y=x^2, x=y^2 about the line x=-5 one year ago one year ago

1. tkhunny Group Title

Find the points of intersection. This will also be your integral limits with this lovely region.

2. monroe17 Group Title

how do i do that?

3. tkhunny Group Title

$$x^{2} = \sqrt{x}$$ -- Solve!

4. monroe17 Group Title

0 and 1 :)

5. tkhunny Group Title

Perfect. Now, decide disks or shells. With this well-behaved region, it really doesn't much matter. Just pick one.

6. monroe17 Group Title

disks

7. tkhunny Group Title

Disks it is, then. $$\pi\int\limits_{0}^{1} OuterRadius^{2} - InnerRadius^{2} d(Height)$$ The "Height" is the x-direction, so we have: $$\pi\int\limits_{0}^{1} OuterRadius^{2} - InnerRadius^{2} dx$$ Now indentify that inner and outer radii. What say you?

8. monroe17 Group Title

x^2+5

9. tkhunny Group Title

Well, I would prefer the more literal (-5-x^2), but it will do since we are just going to square it. Is that the inner or the outer radius?

10. monroe17 Group Title

11. tkhunny Group Title

No worries. x^2 is the inner radius. Are we calling that 'r'? What is the outer radius, "R"?

12. monroe17 Group Title

isn't (-5-x^2) the outer radius? and yes

13. tkhunny Group Title

No, $$x^{2}$$ and $$\sqrt{x}$$ are a little funny on [0,1] $$\sqrt{x} \ge x^2\;for\;x\in[0,1]$$

14. monroe17 Group Title

uhm.. im not sure ;/

15. tkhunny Group Title

r is $$(-5 - x^{2})$$ R is $$(-5 - \sqrt{x})$$ That's all. Did you draw a picture? You will see it at a glance.

16. monroe17 Group Title

I'm still confused toward the sqrt(x) where'd that come from?

17. tkhunny Group Title

x = y^2 ==> y = sqrt(x) We have integration "dx", so we need the representation in terms of x.

18. monroe17 Group Title

got it ;p lol just had to see the steps..

19. tkhunny Group Title

Well, there you have it. Let's see what you get.

20. monroe17 Group Title

I got 109pi/30?

21. tkhunny Group Title

THAT is the right answer. Good work! Wading through it is FUN, isn't it?!

22. monroe17 Group Title

haha.. totally ;p

23. tkhunny Group Title

Once we realized what the region was, and where the square root came from, you were all over it. This is encouraging! Move on to the next one!