Let f(x,y,z) = x be a region bounded above by z = x^2 - y^2 = 4 and below by x^2 + 3y^2 in the octant x%26gt;=0, y%26gt;=0, z%26gt;0. I'm sure I should use spherical coordinates but I have no idea how to find theta, phi, and rho. Help would be much appreciatedHow to set up triple integral?
I suppose the question is to calculate the triple integral of f over the domain x%26gt;=0, y%26gt;=0, z%26gt;0, z%26lt;x^2 - y^2 +4, z%26gt;x^2 + 3y^2. (you should check the part z = x^2 - y^2 = 4 because it makes no sense).
I'm not sure you need to use spherical coordinates. I would first integrate out the z part, since for a given x and y the domain is quite simple: x虏+3y虏%26lt;z%26lt;x虏-y虏+4, and since f does not depend on x, the integral is easy: x*(-4y虏+4) but only if y%26lt;=1.
Then you can integrate by y, since then the domain looks like x%26gt;=0, 0%26lt;=y%26lt;=1, and then you can integrate by x.
Even if the equation for z on the upper boundary is false, you should be able to work your way through the similar steps.
