Show That the Average Value Of $f ( x , y ) = a x + b y$

question 71

Essay

Show that the average value of $f ( x , y ) = a x + b y$ over $R = \{ ( x , y ) \mid - 1 \leq x \leq 1 , - 1 \leq y \leq 1 \}$ is 0 for all values of a and b.

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Definitions:

Promisor

An individual or entity that makes a promise or agreement to perform a specified act or service in a contract.

Delegable

Refers to duties or tasks that can be assigned or transferred from one party (the delegator) to another (the delegatee), legally allowing for the completion of the task by someone other than the original party.

Duty

A moral or legal obligation to perform or refrain from performing a certain action.

Novation

The act of replacing an old obligation with a new one, substituting a new party into an existing agreement or completely replacing the original contract.