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A volume sits above the figure in the $xy$-plane bounded by the equations $y = \sqrt{x}$, $y = −x$ for $0 ≤ x ≤ 1$. Each $x$ cross section is a half-circle, with diameter touching the ends of the curves. What is the volume?

a) Sketch the region in the $xy$ plane.

b) What is the area of a cross-section at $x$?

c) Write an integral for the volume.

d) Find the value of the integral.

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