Find the area of the region bounded by the curves y =arcsin(x/2), y = 0, and x = 2 obtained by integrating with respect to y.

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Graph it.
Looks like it is bounded from x=0 to x=2
\[\int\limits_{0}^{2}\sin^{-1} (x/2)\]

respect to y means leaving the y alone
You are referring to respect to x

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