# 7 73 3 15 24 use the best method available to find

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7 73 3 15 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. a. WA 1, p. 13
.792054 2 0 .792054 .792054 2 0 .792054 2 2 .792054 2 .792054 0 2 .792054 2 2 .792054 0 2 .792054 3 2 2 .792054 0 2 , 1 2 ( 1) 4 4 ( 2 1) 2 4 2 3 2 5.972 x to to to to x x x x x r x r e V V V V x dx e dx V x x dx e e dx x e V x x e x V 7 b.   .792054 2 0 .792054 .792054 2 0 .792054 .792054 2 0 .792054 2 .792054 .792054 0 2 .792054 2 .8 0 2 3 2 2 .792054 , 2 , 1 2 2 2 ( )( 1) 2 2 2 ( ) 2 2 3 2 to to x to to to to x x x r x r x r x r e V V V V x x dx x e dx V x x dx xe x dx x x V x xe .792054 0 14.5 V 26.Use the best method available to find the volume of the region bounded bysinyxand 2 y x revolved about (a) y = 1, (b) x = 1, (c) the y -axis, and (d) the x -axis. a. WA 1, p. 14
2 2 .876726 .876726 2 0 0 .876726 .876726 4 2 2 0 0 .876726 .876726 5 3 0 0 1 1 sin( ) 2 1 sin ( ) 2sin( ) 1 2 sin( )cos( ) 2( cos( )) 5 3 2 2 10.05 V x dx x dx V x x dx x x dx x x x x x V x x x V b.c.d. 2 0876726 2 0 0876726 2 0 0876726 3 2 0 .876726 4 3 0 1 , sin( ) 2 1 (sin( ) ) 2 1 (sin( ) ) 2 sin( ) sin( ) 2 cos( ) sin( ) cos( ) 4 3 .4744 r x h x x V x x x dx V x x x dx V x x x x x dx x x V x x x x V .876726 2 0 .876726 3 0 .876726 4 0 2 ( )(sin( ) ) 2 ( sin( ) ) 2 sin( ) cos( ) 4 .3778 V x x x dx V x x x dx x V x x x V Section 5.4 WA 1, p. 15 3 2 5 2 0 .76 8 7 1 0 0 .7 6 8 70 87 11 00 0 .76 8 7 212 0 2 ( ) (s in 2 s in ( )2 s in ( 21 s in1 2 2 54 1 .6 5 6 9 Vyd y Vydy yy y V V       
4. Approximate the length of the curve using n secant lines for n = 2; n = 4. ln ,1 3 y x x Points for n=2 are 1,2,3 2 2 2 2 (2 1) ( (2) (1)) (3 2) ( (3) (2)) 1.79 s f f f f s 14. Compute the arc length exactly. 2 2ln(4 ), 0 1 y x x 2 2 2 2 1 2 0 1 '( ) ( ) 2ln(4 ) 4 '( ) (4 ) 4 1 (4 ) 1.1972 b a s f x dx f x x x f x x x s dx x s 30. Set up the integral for the surface area of the surface of revolution, and approximate the integral with a numerical method. WA 1, p. 16
sin , 0 , y x x revolved about the x -axis 2 2 0 2 ( ) 1 '( ) 2 sin 1 cos 14.424 b a S f x f x dx S x xdx S 32. Set up the integral for the surface area of the surface of revolution, and approximate the integral with a numerical method.