13) Evaluate the double integral ♫♫ cos(x² + y²) dy dx by rewriting in a different coordinate system. Sketch the region first before doing anything else. 14) Evaluate the double integral ſſxy dA, where R is the region in the first quadrant enclosed by y = √x, y = 6x, and y = 0. Π 15) Evaluate the triple integral √ √cose) √² r sin(e) dz dr do. What is the coordinate system being used in this integral? 16) Use a triple integral to show that the volume of a sphere with radius r ≥ 0 is given by the formula V = 1 ½πr³. 17) Use the Cross-Partial Test to show that the vector field F = (2xy³, 1 + 3x²y²) is a conservative vector field. 18) Find the potential function for each conservative vector field: (a) F(x, y) = (x, y) (b) G(x, y) = (cos(y) + y cos(x), sin(x) − x sin(y)) 19) Evaluate the line integral with respect to s along the parametric curve C: x = t, y = t², z = ²½ t³ ↓ 3x²yz ds C 20) Use the Divergence Theorem to evaluate the surface integral ſſ F · dS, where F = (3x+y, z, 5zx) and S is the boundary of the region between the paraboloid z = 4 − x² − y² and the xy-plane. (Hint: You will need to use a change of variables at some point.)