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Unformatted text preview: (a) Let y = sin x and 0 ≤ x ≤ π . Revolve the region under the curve and above the x-axis. [Note that sin 2 x = 1 / 2-cos(2 x ) / 2.] (b) Let y 1 = 4-x 2 and y 2 = x 2 . Revolve the region between y 1 , y 2 , and the y-axis. (c) Revolve the region enclosed by the circle of radius 1 centered at (0 , 3). Here, just set up an integral that describes the volume of the resulting torus. Also, (d) Find the volume of a right circular cone of height H and base radius R. (e) Find the volume of a solid object with a circular base and square cross sections. Finally, if y 1 = 4-x 2 and y 2 = x 2 , ﬁnd the area of following regions. (f) The region between y 1 , y 2 , and the y-axis, (g) The region between y 1 , y 2 , and the x-axis....
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- Fall '06
- Cone, dx