Around the campfire

Calculus Level 4

Let \(C\) be the anti clockwise semicircle represented by \(x^2 + y^2 = 1, y \geq 0 \). If \(dS\) is the differential of the arc length of the curve, what is the value of

\[ N = \int_C (2+x^2y)\ dS ? \]

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