## Isabel☺ 2 years ago R is bounded by y=0 & y= 4 - x^2 .

1. Isabel☺

suppose it is a parabola: |dw:1359970089368:dw|

2. Isabel☺

@apoorvk

3. Isabel☺

@Callisto

4. Callisto

What is the question?

5. Isabel☺

solve the problem using Disk Method of Solution. Solid V is generated by revolving the given below region R about the x-axis. Draw R and make a sketch of V: R is bounded by y=0 & y= 4 - x^2 .

6. Isabel☺

solve for volume |dw:1359970762069:dw| @Callisto

7. Callisto

Disk method: |dw:1359988516003:dw| $V = \pi \int_a^b r^2 dx = \pi \int_a^by^2dx$ To find a and b, solve the equations y=0 & y= 4 - x^2. (The x values you get will be the value of a and b) $y=4-x^2$ Can you do it now?

8. Isabel☺

a=0 b=4?

9. Isabel☺

can it be like: |dw:1359971017830:dw|

10. Callisto

No.... Solve y=0 and y= 4-x^2 => y = 0 = 4-x^2 So, now, you need to solve 4-x^2 =0 to find a and b.

11. Isabel☺

oh yea right im confused wait...

12. Callisto

^That no was for your first question. You can draw r there.. It doesn't matter where you put the r... since the value of r will be represented by the function y.

13. Callisto

Can you solve a quadratic question?

14. Isabel☺

x= -2 and +2?

15. Callisto

Yes. So, the integral is $V = \pi \int_{-2}^{2} y^2 dx=\pi \int_{-2}^{2} (4-x^2)^2 dx$Can you do it?

16. Isabel☺

maybe wait...

17. Isabel☺

32 pi/ 3?

18. Callisto

Not quite...

19. Isabel☺

oh i forgot to square...

20. Isabel☺

512pi/ 15?

21. Callisto

Yup :)

22. Isabel☺

yey! thank you!! :)

23. Callisto

You're welcome :) Hope that you know how to do it now!

24. Isabel☺

hopefully yes :) thanks again :)