Line integral

Calculus Level 4

Let \(C\) be the enclosed anti clockwise path around the circles \(x^2 + y^2 = 1\) and \(x^2+y^2 = 4\) when \(y \geq 0\) (as shown by the red curves in the figure).

What is the value of \[ \displaystyle \oint_C (y^2\, dx + 5xy\, dy) ? \]

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