Finding the Bounded Region of x=0, y=0, y=x^2, y=4-x^2 and x=2

[cloveryeah]

i m thinking of this...
area bounded by x=0, y=0, y=x^2, y=4-x^2 and x=2

why the region bounded by the below three cases are the same
1. x=0, y=0, y=x^2, y=4-x^2
2. y=0, y=x^2, y=4-x^2
3. and x=0, y=x^2, y=4-x^2

but after i add x=2 and compute the bounded region, it's different?

i am just feeling so hard of finding the bounded region of the above curves

 

[mfb]

Moved to homework section

It is unclear which area you mean. The initial 5 conditions can be used to define up to 5 different areas, and all three cases below are ambiguous as well.

Did you draw a sketch?

 

[cloveryeah]

http://upload.lsforum.net/users/public/z40672Untitledk213.png
y the area bounded is like that
it seems x=2 and x=0 and y=0 don't involve into it

 

[haruspex]

http://upload.lsforum.net/users/public/z40672Untitledk213.png
y the area bounded is like that
it seems x=2 and x=0 and y=0 don't involve into it

This is still unclear.
Do you mean 4 - x² > y > x² & x > 0, or
4 - x² > y > 0 & x² > y, or
something else?

 

[HallsofIvy]

For the initial description,
x=0, y=0, y=x^2, y=4-x^2 and x=2
and the conditions you are given,
1. x=0, y=0, y=x^2, y=4-x^2
2. y=0, y=x^2, y=4-x^2
3. and x=0, y=x^2, y=4-x^2
Note, that in "1" the three conditions given are exactly the same as in the initial description. You have to explain why "x= 2" is not necessary.
For "2" the same is true except that it is "x= 0" that is missing and for "3" it is y= 0.