# Sketch the region draw in a typical shell identify

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6. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute the volume for the region bounded by 2 y x and 0, 1 1 y x , revolved about x = 2 .
8. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute the volume for the region bounded by 2 2 2 x y y .
12. Use cylindrical shells to compute the volume of the region bounded by 2 x y and x = 4 , revolved about y = 2 .
22. Use the best method available to find the volume of the region bounded by 2 2 , ( 0) y x y x x and the y -axis revolved about (a) the x -axis, (b) the y -axis, (c) x = –1, and (d) y = –1.
24. Use the best method available to find the volume of the region bounded by 1, 2 x y e y x and the x-axis revolved about the (a) x -axis and (b) y -axis.
b) V = 0 .792 2 π ( x )( | 2 x e x 1 | ) dx = π ( 6 ( x 1 ) e x + x 2 )( 2 x 3 ) 3 2.4677 calculated using TI-nspire
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