The body K is limited by the cone z= -sqrt(x^2+y^2) and the sphere x^2+y^2+z^2=16
Now, the most natural thing to do is to introduce spherical coordinates:
In this case, the body K would be described by:
cone z= -sqrt(x^2+y^2)--> -sqrt(r^2(sinω)^2)= - rsinω
and x^2+y^2+z^2=16 --> r^2= 16
z= rcosω = -rsinω --> ω= -pi/4
which means that the limits of the integral is
(is this correct?)
However, the task states that I should use cylindrical coordinates to describe the body K:
Then the body K would be described as: the cone = -r and the sphere = r^2 + z=16
But which limits do I set here?
Is this correct, is the transformation to cylindrical spheres this easy when they ask for the body K to be described by cylindrical coordinates?