## Isabel☺ Group Title R is bounded by y=0 & y= 4 - x^2 . one year ago one year ago

1. Isabel☺ Group Title

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

2. Isabel☺ Group Title

@apoorvk

3. Isabel☺ Group Title

@Callisto

4. Callisto Group Title

What is the question?

5. Isabel☺ Group Title

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☺ Group Title

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

7. Callisto Group Title

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☺ Group Title

a=0 b=4?

9. Isabel☺ Group Title

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

10. Callisto Group Title

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☺ Group Title

oh yea right im confused wait...

12. Callisto Group Title

^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 Group Title

Can you solve a quadratic question?

14. Isabel☺ Group Title

x= -2 and +2?

15. Callisto Group Title

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☺ Group Title

maybe wait...

17. Isabel☺ Group Title

32 pi/ 3?

18. Callisto Group Title

Not quite...

19. Isabel☺ Group Title

oh i forgot to square...

20. Isabel☺ Group Title

512pi/ 15?

21. Callisto Group Title

Yup :)

22. Isabel☺ Group Title

yey! thank you!! :)

23. Callisto Group Title

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

24. Isabel☺ Group Title

hopefully yes :) thanks again :)