Find the volume of the solid that lies under the hyperbolic paraboloid
z = 3y^2 − x^2 + 5
and above the rectangle
R = [−1, 1] × [1, 2].
Find the average value of f over the given rectangle.
f(x, y) = 2x^2y, R has vertices (−4, 0), (−4, 5), (4, 5), (4, 0).