Math 210 E1 S92 — Calculus III — Exam #3 (Ch. 13) — Hanson — page 1 of 2 Show work on this sheet in 50 minutes (5 × 20 = 100 points).

Name  .  SocSecNo.  .

1. Evaluate ∫_{0}^{π/2} dx ∫_{0}^{1} dy x · sin(xy) =

2. Evaluate ∫_{0}^{1} dy ∫_{y}^{1} dx sin(x^{2}) =

3. On 4 ≤ x^{2} + y^{2} ≤ 9, evaluate ∫ ∫_{R} dA cos(x^{2} + y^{2}) =

Math 210 E1 S92 — Calculus III — Exam #3 — Hanson — page 2 of 2

4. On 4 ≤ x^{2} + y^{2} + z^{2} ≤ 9 in the first quadrant, evaluate ∫ ∫ ∫_{R} dV (x^{2} + y^{2} + z^{2})^{100} =

5. Evaluate ∫ ∫ ∫_{R} dV z^{3} over the region bounded by x^{2}/a^{2} + y^{2}/b^{2} + z^{2}/c^{2} = 1,

using x/a = u · cos(v) sin(w), y/b = u · sin(v) sin(w), and z/c = u · cos(w), with

∂(x, y, z)/∂(u, v, w) = a · b · c · ∂(x/a, y/b, z/c)/∂(u, v, w)

.