Find a function F(x, y) satisfying  and use the result of Exercise 52 to evaluate  for R = [0, 1] × [0, 4].

Data From Exercise 52

Prove the following extension of the Fundamental Theorem of Calculus to two variables: If ∂²F/∂x ∂y = ƒ(x, y), then

where R = [a, b] × [c, d].

8F = 6x