## Frostbite 3 years ago Can some fast calculate the double integral using polar coordinates and cartesian coordinates? D={(x,z,y)|-1≤x≤0,-√(1-x^2 )≤y≤√(1-x^2 )} f(x,y,z)=x^2

1. Frostbite

i got the answer to π/8 and 1, but that can't be true?

2. experimentX

|dw:1352299213766:dw|

3. experimentX

if expression is like above then just evaluate it with usual process ... doesn't seem that difficult.

4. Frostbite

not quite sure i understand. i mean on polar coordinates the set would be: Dp={(x,z,y)┤|-1≤r≤0 ,π/2≤θ≤3π/2} right? and then the following (see file)

5. experimentX

how did you change the limits?

6. experimentX

|dw:1352299738473:dw|

7. Frostbite

don't know if you can see it but there is a square root around 1-x^2

8. Frostbite

well the reason why i set my limit for theta to that is becuase the set should look like something like this: |dw:1352300003766:dw|

9. Frostbite

Unless i have misunderstod something?

10. TuringTest

it's the left half of a circle, I agree

11. experimentX

sorry .. i completely missed sqrt() ..

12. Frostbite

well kinda my falt i should have written sqrt() .. insted of √(1-x^2

13. TuringTest

what bounds did you use?

14. experimentX

|dw:1352300314417:dw|

15. TuringTest

yeah, that's what I got

16. TuringTest

oh no, r^3 though...

17. Frostbite

is it not r^2?

18. TuringTest

you have r^2 from the x^2 and r from dA

19. experimentX

yeah .. it's r^3

20. Frostbite

can evne find that in my book that extra r, but seems to be right yea

21. Frostbite

can't* even*

22. Frostbite

But is this polar set wrong then? Dp={(x,z,y)┤|-1≤r≤0 ,π/2≤θ≤3π/2}

23. experimentX

$dx \;dy = r \; dr \; d\theta$

24. Frostbite

no wait can see it my self.. it is just 0<=r<=1

25. TuringTest

right, the angle covers the negative part

26. TuringTest

I still get pi/8 by the way...

27. Frostbite

Just think i need to take a few more looks becuase i keep geting a wrong result.

28. Frostbite

So we can all agree to this: (sorry for have pulling both you through all thís)

29. TuringTest

That's what I got

30. Frostbite

Alright thanks alot to both of you.

31. TuringTest

Welcome.