Evaluate the Cylindrical Coordinate Integral $\int _ { 0 } ^ { \pi / 2 } \int _ { 4 } ^ { 8 } \int _ { 1 / r ^ { 2 } } ^ { 1 / r } z \cos \theta d z r d r d \theta$

question 301

Multiple Choice

Evaluate the cylindrical coordinate integral.
- $\int _ { 0 } ^ { \pi / 2 } \int _ { 4 } ^ { 8 } \int _ { 1 / r ^ { 2 } } ^ { 1 / r } z \cos \theta d z r d r d \theta$

• A) \(\frac { 64 \ln 2 - 3 } { 256 }\)
• B) \(\frac { 64 \ln 2 - 6 } { 256 }\)
• C) \(\frac { 128 \ln 2 - 6 } { 256 }\)
• D) \(\frac { 128 \ln 2 - 3 } { 256 }\)

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