(18 - ab) + 4b (if a = -2 and b = -5)
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Answer
given,
interval = [-32, 32]
differentiating the given equation
hence, the above solution is not defined at x = 0
and x = 0 lie in the given interval i.e. [-32, 32]
so, at x = 0 the function is not differentiable.
Hence, mean value theorem does not apply to the given function.
In Cartesian coordinates, the region is given by 
, 
, and 
. Converting to cylindrical coordinates, using
we get a Jacobian determinant of
, and the region is given in cylindrical coordinates by 
, 
, and 
.
The volume is then
we get a Jacobian determinant of
The volume is then