Part 3 Answer the following integral calculus questions:

(i) Consider the double integral:

(j) A person holds up an umbrella to protect against the falling rain. There is no wind, so the rain is falling completely vertically. The umbrella has a radius of 1 m and the height of the umbrella surface at any point is given by: f(x,y)=3-x²-y²

The centre of the umbrella can be assumed at be at z=y=0. Find the volume of dry space under the umbrella using an integral in terms of polar coordinates.