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The region is bounded by y=2−x^2 and y=x. (a) Sketch the region. (b) Find the area...

The region is bounded by y=2−x^2 and y=x. (a) Sketch the region. (b) Find the area of the region. (c) Use the method of cylindrical shells to set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region about the line x = −3. (d) Use the disk or washer method to set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region about the line y = 3.

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