# Let r be the region bounded by 2 y x and y 4 compute

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26.Let Rbe the region bounded by 2 y x and y = 4 . Compute the volume of the solid formed by revolving R about the given line. (a)y= 4(b) the y-axis(c) y= 6(d) y= –2(e) x= 2(f) x= –4 a. b. WA 1, p. 7 2 2 2 2 2 2 4 2 2 2 2 5 3 2 ,4 4 816 256256512 816 5 151515 b a Vrdxrx V xdx xxdx xx V x x          2 2 4 4 0 0 4 2 0 , 8 2 b a V r d y x y V y d y y d y y V
c. d. 2 2 0 2 2 2 2 2 2 2 2 2 4 2 2 2 2 5 3 15 15 2 2 2 4 ( 2) 6, ( 2) 2 6 2 36 4 4 4 376 376 36 4 72 72 5 3 15 15 2160 752 1408 15 15 15 i r r x x V dx x dx V dx x x dx x x V x x V     e. WA 1, p. 8 6 , 6 4 2 6 2 1 2 3 6 4 1 2 3 6 4 5 3 2 3 2 2 3 2 3 8 4 8 8 5 5 5 r x r V x d x d x V x x d x d x x x V x x V 3 3 2 2 4 4 2 2 0 0 4 4 0 0 4 4 2 2 0 2 , 2 (2 ) (2 ) 4 4 ( 4 4) 8 8 4 4 2 3 2 3 136 8 128 3 3 3 o i o r yr y V y dy y dy V y y dy y y dy y y y y V y y V    
f. 3 3 2 2 4 4 0 0 4 4 0 0 4 4 2 2 2 2 0 0 4, 4 4 4 8 16 8 16 16 16 16 16 2 3 2 3 344 88 256 3 3 3 o i r y r y V y dy y V y y dy y y dy y y y y V y y V 32. Suppose that the circle 2 2 1 x y is revolved about the y -axis. Show that the volume of the resulting solid is 4 3 . 2 2 1 1 2 2 1 1 1 1 2 1 1 1 3 1 1 1 1 1 1 1 1 1 3 3 3 2 2 4 3 3 3 r y V y dy y dy V dy y dy y V y V   Section 5.3 4. 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 , , y x y x   and 1, x revolved about 1 x . WA 1, p. 9   1 1 0 0 1 3 1 2 0 0 2 () ,() (() , 2 2 2 1 4 4 4 40 3 3 3 b a V xfxdx xrad iu sfxhe igh txxdxth icknes V xxxdx xxdx x V xdx                      
6. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and