SOLUTION: What is the area of the region bounded by the curves {{{ y = arcSin(x) + x - x^2 }}} and {{{ y = arcSin(x) - x + x^2 }}} in the first quadrant and in the second quadrant?

Question 1184303: What is the area of the region bounded by the curves and in the first quadrant and in the second quadrant?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

A quick check with Desmos online graphing shows that the region bounded by
and involves quadrants 1, 2, and 3,
so I will just assume that you just made some kind of transcription error.
First find intersection points of the two curves.
===> ===> x = 0, 1.
Over [0,1], , and so the area of the region between them is given by

Over [-1,0], , and so the area of the region between them is given by

.

Therefore the combined area of the region between the two curves is .

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