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15.5E: Ejercicios para la Sección 15.5
https://espanol.libretexts.org/Matematicas/Libro%3A_Calculo_(OpenStax)/15%3A_Integraci%C3%B3n_m%C3%BAltiple/15.05%3A_Integrales_triples_en_coordenadas_cil%C3%ADndricas_y_esf%C3%A9ricas/15.5E%3A_Ejercicios_para_la_Secci%C3%B3n_15.5
Show that if $F ( \rho,\theta,\varphi) = f(\rho)g(\theta)h(\varphi)$ is a continuous function on the spherical box \(B = \big\{(\rho,\theta,\varphi)\, | \,a \leq \rho \leq b, \space \alpha \leq \the...Show that if $F ( \rho,\theta,\varphi) = f(\rho)g(\theta)h(\varphi)$ is a continuous function on the spherical box $B = \big\{(\rho,\theta,\varphi)\, | \,a \leq \rho \leq b, \space \alpha \leq \theta \leq \beta, \space \gamma \leq \varphi \leq \psi\big\}$ , then $\displaystyle\iiint_B F \space dV = \left(\int_a^b \rho^2 f(\rho) \space dr \right) \left( \int_{\alpha}^{\beta} g (\theta) \space d\theta \right)\left( \int_{\gamma}^{\psi} h (\varphi) \space \sin \varphi \space d\varphi \right).$

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