Evaluate the Cylindrical Coordinate Integral $\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { \cos ^ { 2 } \theta } \int _ { 3 r ^ { 4 } } ^ { 9 r ^ { 4 } } z \sin \theta d z r d r d \theta$

question 233

Multiple Choice

Evaluate the cylindrical coordinate integral.
- $\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { \cos ^ { 2 } \theta } \int _ { 3 r ^ { 4 } } ^ { 9 r ^ { 4 } } z \sin \theta d z r d r d \theta$

• A) \(\frac { 39 } { 70 }\)
• B) \(\frac { 1 } { 8 }\)
• C) \(\frac { 6 } { 35 }\)
• D) \(\frac { 51 } { 140 }\)

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