Engineering Mathematics 233 Solutions: Double and triple integrals

The part of the cone above the xy-plane corresponds to φ = 4π 6 .z sphere x 2 + y 2 + z 2 = 1Btop part of conez 2 = 3(x 2 + y 2 )yxThen, in spherical coordinates, the region B isB : 0 ≤ ρ ≤ 10 ≤ φ ≤ π 60 ≤ θ ≤ 2π.Then,∫ ∫ ∫ √x2+ y 2 + z 2 dV === 1 4= 1 4= 1 4(=∫ 2π ∫ π/6 ∫ 10 0∫ 2π ∫ π/60 0∫ 2π ∫ π/60∫ 2π0∫ 2π01 −ρ ρ 2 sin φ dρ dφ dθ0()ρ 4 1sin φ4 ∣ dφ dθsin φ dφ dθ0()π/6− cos φ∣ dθ0√31 −2 dθ√ )3 π2 2 .018