MATH 551 Midterm: Kansas State MATH 551 551t2s99

5. Find the value of k that makes (x^2y^3 + kx^3y)dx + (z + y^2)x^3dy = 0 an exact differential equation. (a) k = 0 (b) k = 1 (c) k = 2 (d) k = 3 (e) k = 4

1. (3 points) Evaluate 2xd where W is the region under the plane 2x +3y+ z = 5 in the first octant. x=3y, x = 0, and z = 0. x2 + y-2 as the side, and the plane = 3-x-y as the top 2, (4 points) Calculate the volume of the solid bounded by the graphs x+ 2y+ z = 2, 3, (4 points) Find the volume of the solid with plane z = 0 as the bottom, the cylinder