Chapter 6 | Applications of Integration
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Figure 6.36 (a) The region R between the curve and the x -axis. (b) The solid of revolution generated by revolving R about the x -axis.
Looking at the region, it would be problematic to define a horizontal rectangle; the region is bounded on the left and right by the same function. Therefore, we can dismiss the method of shells. The solid has no cavity in the middle, so we can use the method of disks. Then V = ∫ 0 4 π ⎛ ⎝ 4 x − x 2 ⎞ ⎠ 2 dx .
6.17 Select the best method to find the volume of a solid of revolution generated by revolving the given region around the x -axis, and set up the integral to find the volume (do not evaluate the integral): the region bounded by the graphs of y =2− x 2 and y = x 2 .
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