211 Let E denote the region above the paraboloid z x2 y2 a

2.11) Let E denote the region above the paraboloid z = x^2 + y^2 and below the half-cone
z = x^2 + y^2.

(b) Set up (butdo notevaluate) the triple iterated integral in spherical coordinates for <?xml:namespace prefix = o ns = \"urn:schemas-microsoft-com:office:office\" /?>

the volume of the region E.

Solution

earlier in cylindrical coordinates

x = r cos , y = r sin , z = z, dV = rdrddz.

now spherical coordinates

x = sincos , y = sinsin , z = cos, dV = ²sinddd

just change the limits appropriately for these values of ,, from the earlier solution