2. (15pts each) Find the volumes of the solid by rotating about the region bounded by the curves using the specified method (a) Use Cylindrical-Shell Method to find the volume of the solid obtained by rotating the region bounded by the given curves about the $x$-axis. Given $x = 1 + (y - 2)^2$ and $x = 2$ (b) Use Disk/Washer Method to find the volume of the solid obtained by rotating the region bounded by the given curves about the $y = 1$. Given $y = 1 + secx$ and $y = 3$
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To find the points of intersection, set the two equations equal to each other: 1 + √x = 3 √x = 2 x = 4 So the two curves intersect at x = 4. Show more…
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