Set up the double integral in rectangular coordinates for calculating the volume.
The solid is created by the equation
Fubini's Thereom ∫R∫f(x,y)dA = ∫ab∫f(x,y)dydx
The Attempt at a Solution
The shape created by Z = 30 - x2 - y2 is 3d parabola facing downards.
Since it is bounded by Z = 5, the base shape is a circle at origin with radius 5 since
5 = 30 - x2 - y2 is equal to x2 + y2 = 25
As a result x is bounded by -5 and 5 while y is bounded by -√(25-x^2) and √(25-x^2)
As a result to set up the double integral
Are the integral boundaries in correct?