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Evaluate , If C Is the Path Shown Below

Question 147

Short Answer

Evaluate ∮C(14y4−12x3cos⁡y3)dx+(xy3+x2+38x4y2sin⁡y3)dy\oint _ { C } \left( \frac { 1 } { 4 } y ^ { 4 } - \frac { 1 } { 2 } x ^ { 3 } \cos y ^ { 3 } \right) d x + \left( x y ^ { 3 } + x ^ { 2 } + \frac { 3 } { 8 } x ^ { 4 } y ^ { 2 } \sin y ^ { 3 } \right) d y , if C is the path shown below. Evaluate \oint _ { C } \left( \frac { 1 } { 4 } y ^ { 4 } - \frac { 1 } { 2 } x ^ { 3 } \cos y ^ { 3 } \right) d x + \left( x y ^ { 3 } + x ^ { 2 } + \frac { 3 } { 8 } x ^ { 4 } y ^ { 2 } \sin y ^ { 3 } \right) d y , if C is the path shown below.

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