Find the area of the shaded region?

This is a parabola with vertex (0,1)

Because it opens up it is of the form

(y - 1) = ax^2

Since (-1,0) and (1,0) are on this parabola (y - 1) = x^2

0
? (1 - (x^2) dx = x - (x^3/3) = 0 - 0 -(-1) -(-(-1/3)) = 1 - (1/3) = (2/3) <---- Answer

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