ok from that, i think i can see that x is from 0 to root(1-y^2), y is from 0 to 1 and z is from 0 to 2y.. so they are bounds of my region.
sketch the following region in R3
V={r:y>=0,0<=x^2+y^2<=1,0<=z<=2y}
ok i have that xy plane is a quarter circle, on the zy plane is the line z=2y.. im trying to picture but i just cant, im thinking its like a quarter cone, but the apex is not at (0,0,0) please can anyone try and draw it for me?
ok, have been thinking now an can plz someone confirm, or help with this..
on xy plane x^2+y^2=1 is semicircle with radius 1. but is constriced to a quarter circle because x [0,1] and y [0,1], on the yz plane, the line z=2y... putting them together gives an upside down quarter cone.... i think, but not sure because wouldnt that imply that z=2x as well?
I can see nowhere that you said that x was restricted to [0,1]. Knowing that [tex]x^2+ y^2= 1[/itex] and that [itex]y\ge 0[/itex] only tells you that [itex]-1\le x\le 1[/itex]. Also z= 2y is not a line it is a z plane. And, no, z= 2y does not mean z= 2x because x in not, in general, equal to y. The solid has a half circle base with the plane z= 2y a top, extending from the x-axis up to the point (0, 1, 2).
This is not, however, a bounded region because you have not specified a "bottom". Are you also requiring, say, ?