Unformatted text preview: Calculus III Section 13.7 – Triple Integrals in Cylindrical and Spherical Coordinates
As we have already seen many integrals are easier to integrate if we use cylindrical or spherical coordinates
instead of rectangular coordinates. In this section we will just practice integrating in the other coordinate
Cylindrical Coordinates ∫ Q ∫ f∫( x, y, z )dV = θ 2 g 2 ( θ ) h2 ( r cos θ , r sin θ ) ∫∫ ∫ f (r cosθ , r sin θ , z )rdzdrdθ θ1 g1 ( θ ) h1 ( r cos θ , r sin θ ) Since we have already integrated many iterated integrals in cylindrical coordinates we will just go ahead and
practice one in spherical coordinates together. The cylindrical coordinate integrals in this section are no
different than the ones we have already done.
Spherical Coordinates ∫ Q ∫ f∫( x, y, z )dV = Example: θ 2 φ2 ρ 2s ∫ ∫ ∫ f ( ρ sin φ cosθ , ρ sin φ sin θ , ρ cos φ ) ρ
1 π /4 π /4 cos θ 0 0 ∫∫∫
0 1 1 ρ 2 sin φ cos φ dρ dθ dφ 2 sin φ dρ dφ dθ ...
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This note was uploaded on 01/13/2012 for the course MATH 2574 taught by Professor Pamelasatterfield during the Spring '12 term at NorthWest Arkansas Community College.
- Spring '12