1. Homework problems for test 4 review –backward. Do the following problems
Green’s Theorem pg 964. 1 – 11 odd (Just do the calculation for circulation,
i.e. theorem 4 on pg 958. )
Conservative fields and Potential functions –posted hw 29 on, do 17, 18, 19, 23, 25, 27
Line integrals Pg 935: 9, 10, 11
Spherical coordinate: Triple integral setups over common solids shown on the next page.
Triple integrals in the rectangular coordinate pg. 904: 3, 4, 19, 20
Triple integrals in the rectangular coordinate pg. 904: 3, 4, 19, 20
Double integrals in the rectangular coordinate and reversing the order of integration.
pg. 885: 1, 3, 5, 7, 21, 25, 29, 31, 33

2. a
b
a
{a ≤ ρ ≤ b, 0 ≤ θ <2π, 0 ≤ φ ≤ c}
b
{sec(φ)a ≤ ρ ≤ b, 0 ≤ θ <2π, 0 ≤ φ <c}
A cup cake
{a ≤ ρ ≤ b,
0 ≤ θ <2π,
0 ≤φ<π}
{a ≤ ρ ≤ a + Δρ,
b ≤ θ ≤ b + Δθ,
c ≤ φ ≤ c + Δφ}
a
θ=b
φ=c
{0 ≤ ρ ≤ r,
a ≤ θ ≤ b,
0 ≤ φ ≤ π}
{0 ≤ ρ ≤ r,
a ≤ θ ≤ b,
0 ≤φ<π}
a
b
{sec(φ)a ≤ ρ ≤ sec(φ)b, 0 ≤ θ <2π, 0 ≤ φ <c}
A paper cup
Δθ
Know the spherical description of the following common
spherical coordinate solids.