# Calculation of area

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Consider the function defined by the equation $\mathbf{ y^2-2y.e^{sin^{-1}x}+x^2-1+[x]+e^{2sin^{-1}x} = 0}$, Where $\mathbf{[x] = }$ Greatest Integer function.

The find area of the curve bounded by the curve and the equation $\mathbf{x = -1}$

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If real domain is considered then I guess $x \in [-1, 1]$?

I would try numerically. Is $\int$ close to 3?

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I got 4.14159 using the following Mathematica code:

Abs[NIntegrate[E^ArcSin[x] - Sqrt[1 - x^2 - Floor[x]], {x, -1, 0}]] +
NIntegrate[E^ArcSin[x] + Sqrt[1 - x^2 - Floor[x]], {x, -1, 1}] -
NIntegrate[E^ArcSin[x] - Sqrt[1 - x^2 - Floor[x]], {x, 0, 1}]

Although I've no idea if it's correct.

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I got 4.14159 using the following Mathematica code:

Abs[NIntegrate[E^ArcSin[x] - Sqrt[1 - x^2 - Floor[x]], {x, -1, 0}]] +
NIntegrate[E^ArcSin[x] + Sqrt[1 - x^2 - Floor[x]], {x, -1, 1}] -
NIntegrate[E^ArcSin[x] - Sqrt[1 - x^2 - Floor[x]], {x, 0, 1}]

Although I've no idea if it's correct.

Looks suspiciously close to $\pi + 1$..

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