Mathematics, 24.09.2019 00:50 SPDrac0
Evaluate e y2z2 dv, where e lies above the cone ϕ = π/3 and below the sphere ρ = 1.
Answers: 1
as well as;Below the sphere 
![\mathbf{\implies \int ^{2 \pi}_{0} \int ^{\dfrac{\pi}{3}}_{0} \ sin^3 \phi cos^2 \phi sin^2 \theta \Big [ \dfrac{\rho^7}{7} \Big]^1_0 \ d \phi d \theta }](/tpl/images/0256/5662/776f7.png)
![\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{cos^5 \phi}{5}- \dfrac{cos ^3 \phi}{3} \Bigg ] ^{\dfrac{\pi}{3}}_{0} d \theta }](/tpl/images/0256/5662/7c3d4.png)
![\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{cos^5 \dfrac{\pi}{3}}{5}- \dfrac{cos ^3 \dfrac{\pi}{3}}{3}- \dfrac{cos^5 0}{5}+ \dfrac{cos^3 0}{3} \Bigg ] d \theta }](/tpl/images/0256/5662/08538.png)
![\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{2}{15}- \dfrac{17}{480} \Bigg ] d \theta }](/tpl/images/0256/5662/06e51.png)
![\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{(480\times 2) -(15\times 17)}{15\times 480}\Bigg ] d \theta }](/tpl/images/0256/5662/867fc.png)
![\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{705}{15\times 480}\Bigg ] d \theta }](/tpl/images/0256/5662/919f5.png)
![\mathbf{\implies \dfrac{47}{6720} \Bigg [\theta - \dfrac{sin 2 \theta }{2}\Bigg] ^{2 \pi}_{0}}](/tpl/images/0256/5662/83b43.png)
![\mathbf{\implies \dfrac{47}{6720} \Bigg [2 \pi\Bigg] }](/tpl/images/0256/5662/3f983.png)
is given by the set
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Evaluate e y2z2 dv, where e lies above the cone ϕ = π/3 and below the sphere ρ = 1....
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