## SABREEN 3 years ago could i get some help with this?

1. hartnn

@TuringTest ,can u plz try this ?

2. TuringTest

you need the intersection of the two shapes, have you got that yet?

3. SABREEN

nope...

4. TuringTest

set formulas for z equal and find what shape the intersection is

5. SABREEN

a circle with a radius of 4

6. SABREEN

the shape of intersection

7. SABREEN

then..?

8. TuringTest

then what are the bounds on r and theta?

9. SABREEN

0<r<4 and 0<theta<2 pi

10. SABREEN

what do i integrate over though??

11. TuringTest

z upper - z lower

12. TuringTest

which function is on top and which is below for z?

13. SABREEN

r-(32-r^2)^(1/2)

14. TuringTest

yes

15. SABREEN

yea i never know when a function is on top or on the bottom can we plug in values to figure this out?

16. TuringTest

sure, try x=y=0 and you can find out real quick

17. TuringTest

oh, and I see I let you do it backwards, sorry

18. SABREEN

i got it right but i guessed...whats the math behind it?

19. TuringTest

hooray :) at the origin x=y=0, so z=x^2+y^2=0 is on the bottom, and z=32-x^2-y^2=32 is on top

20. SABREEN

hmm i get it plug in x=y=0 to find out which ones on top which ones on the bottom

21. SABREEN

=)!

22. SABREEN

could you have a look at the second question as well

23. TuringTest

by plugging in x=y=0 and comparing values we are asking which one is on top at that point. Unless they cross each other that goes for the whole shape the second one looks a little harder, let me see...

24. TuringTest

|dw:1352743460102:dw|

25. TuringTest

a strip of the shaded area is|dw:1352743660838:dw|

26. SABREEN

yup with u

27. TuringTest

sorry that's|dw:1352743785867:dw|

28. SABREEN

how did u get the equation of the strip

29. TuringTest

|dw:1352743918863:dw|

30. SABREEN

i got the first equation when i apply the top-bottom rule

31. TuringTest

right, but I think we want to do this in polar anyways

32. SABREEN

yea we do so the bottom equation is right because we want to subtract one to gt the bottom half of the circle

33. SABREEN
34. SABREEN