A calculus problem by Dharani Chinta

Calculus Level 4

Let \(y=g(x)\) be the image of \(f(x)=x+\sin x\) about the line \(x+y=0\).

If the area bounded by \(y=g(x)\), \(x\)-axis, \(x=0\) and \(x=2 \pi\) is \(A\), find \(\lfloor A \rfloor\).

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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