If fxy Greaterthanorequalto k for all ay in R a b times cd

If f(x,y) Greaterthanorequalto k for all (a\\y) in R = [a, b] times [c,d], then the volume of the solid that lies above R and between the graphs of z = f(x,y) and z = k is V = f(x,y)dA-k.

Solution

easy to see from graph

f(x,y) - k is the length of vertical linesegment .

we want to integrate this over the area to get volume