Question

Find the volume of the solid region E bounded by the paraboloids z = 1+x^2+y^2 and z = 4 - 2x^2 - 11y^2

Answer 1

the intersection is not a circle but an eclipse so i tried using casterian coordinated but its very ugly and i dont think thats the way ur suppose to do it

Answer 2

my first instinct since both equate to "z" is to equate them and simplify ...

Answer 3

z = 1 + x^2 + y^2
z = 4 - 2x^2 - 11y^2

1 + x^2 + y^2 = 4 - 2x^2 - 11y^2
+4 +4
---------------------------------
5 + x^2 + y^2 = -2x^2 - 11y^2
+2x^2 +2x^2
--------------------------------
5 + 3x^2 + y^2 = - 11y^2
+11y^2 +11y^2
------------------------------
5 + 3x^2 + y^2 = 0

Answer 4

but an elipse is not measured by volume is it

Answer 5

but that should be the "points" of intersection