Evaluate the Integral$\int _ { 0 } ^ { \pi } \int _ { ( 1 - \sin \varphi ) / 2 } ^ { ( 1 - \cos \varphi ) / 2 } \int _ { 0 } ^ { 4 \pi } \varrho ^ { 2 } \sin \varphi \mathrm { d } \theta$

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The Answer of Evaluate the Integral$\int _ { 0 } ^ { \pi } \int _ { ( 1 - \sin \varphi ) / 2 } ^ { ( 1 - \cos \varphi ) / 2 } \int _ { 0 } ^ { 4 \pi } \varrho ^ { 2 } \sin \varphi \mathrm { d } \theta$

Evaluate the Integral De $\mathrm { d } \varphi$ A) $\frac { 1 } { 24 } \pi ( 15 \pi - 16 )$

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Evaluate the Integral De dφ\mathrm { d } \varphidφ A) 124π(15π−16)\frac { 1 } { 24 } \pi ( 15 \pi - 16 )241​π(15π−16)

Definitions:

Evaluate the Integral De $\mathrm { d } \varphi$ A) $\frac { 1 } { 24 } \pi ( 15 \pi - 16 )$