Find the Maximum Value Of $\int _ { C _ { 1 } } y ^ { 3 } d x + \left( 225 x - x ^ { 3 } \right) d y , \text { where } C \text { is any closed curve }$

question 58

Multiple Choice

Find the maximum value of $\int _ { C _ { 1 } } y ^ { 3 } d x + \left( 225 x - x ^ { 3 } \right) d y , \text { where } C \text { is any closed curve }$ in the xy-plane, oriented counterclockwise.

• A) \(\frac { 3357 \pi } { 2 }\)
• B) \(\frac { 4293 \pi } { 2 }\)
• C) \(\frac { 3807 \pi } { 2 }\)
• D) \(\frac { 3843 \pi } { 2 }\)
• E) \(\frac { 2907 \pi } { 2 }\)

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