Suppose that f(x, y) = 2x + 2y and the region D is given by {(x, y) | −4 ≤ x ≤ 1, −4 ≤ y ≤ 1}. D Then the double integral of f(x, y) over D is | | f(x, y)dady = D

A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.

5. Prove that the equation has no solution in an ordered integral domain.

Verify Green's Theorem by evaluating both integrals y² ax + x² dy = x dy /R. ax ду for the given path. C: rectangle with vertices (0, 0), (6, 0), (6, 7), and (0, 7) y2 dx + x² dy : dA = R. dy