Math  /  Geometry

Question9. Considere o sólido que está no primeiro octante, limitado (acima) pela esfera x2+y2+z2=9x^{2}+y^{2}+z^{2}=9, lateralmente pelo cone z=βx2+y2)z=\sqrt{\left.\beta x^{2}+y^{2}\right)}. Em cada item, determine as integrais que permitem calcular o volume desse sólido. a) Em coordenadas cilindricas. b) Em coordenadas esféricas.

Studdy Solution
Configurar a integral tripla em coordenadas esféricas:
V=0π20tan1(β)03ρ2sinϕdρdϕdθ V = \int_{0}^{\frac{\pi}{2}} \int_{0}^{\tan^{-1}(\sqrt{\beta})} \int_{0}^{3} \rho^2 \sin \phi \, d\rho \, d\phi \, d\theta

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