v/x, y = 0 and x = 1. Region bounded by: y Rotate about: (a) the x-axis (b) y=1
ID: 2888704 • Letter: V
Question
v/x, y = 0 and x = 1. Region bounded by: y Rotate about: (a) the x-axis (b) y=1 (c) the y-axis (d) x=1 13. Region bounded by: y = 4-2 and y-o. 20. A righ a righ Rotate about: (a) the x-axis (b) y=4 (c) y=-1 (d) x=2 14. The triangle with vertices (1, 1), (1,2) and (2,1) Rotate about: 4 (a) the x-axis (c) the y-axis (d) x=1 (b) y 2 A sc lar t the 21. Region bounded by y = x2-2x + 2 and y = 2x-1. Rotate about: 15, (a) the x-axis (b) y=1 (c) y=5 16.region bounded by y 1/Vx2+1, x =-1.x = 1 and the x-axis. Rotate about: (a) the x-axis (b) y = 1 (c) y =-1 Region bounded by y = 2x, y Rotate about: x and x = 2. (a) the x-axis (c) the y-axisExplanation / Answer
multiple questions posted.please post each question seperately
14)
equations of lines joining (1,1),(1,2),(2,1) are x=1 , y =1 , y =-x+3
region is 1 x 2 , 1 y -x+3
(a)
by washer method:
volume = [1 to 2]((-x+3)2-(1)2) dx
volume = [1 to 2](x2-6x+8) dx
volume = |[1 to 2]((1/3)x3-3x2+8x)
volume = ((1/3)23-3*22+8*2) -((1/3)13-3*12+8*1)
volume = (4/3)
(b)
by washer method:
volume = [1 to 2]((2-1)2-(2-(-x+3))2) dx
volume = [1 to 2](1-(-1+x)2) dx
volume = [1 to 2](2x-x2) dx
volume = |[1 to 2](x2-(1/3)x3)
volume = (22-(1/3)23) -(12-(1/3)13)
volume = (2/3)
(c)
region is 1 x -y+3 , 1 y 2
by washer method:
volume = [1 to 2]((-y+3)2-(1)2) dy
volume = [1 to 2](y2-6y+8) dy
volume = |[1 to 2]((1/3)y3-3y2+8y)
volume = ((1/3)23-3*22+8*2) -((1/3)13-3*12+8*1)
volume = (4/3)
(d)
by washer method:
volume = [1 to 2](((-y+3)-1)2) dy
volume = [1 to 2](-y+2)2 dy
volume = [1 to 2](y2-4y+4) dy
volume = |[1 to 2]((1/3)y3-2y2+4y)
volume = ((1/3)23-2*22+4*2) -((1/3)13-2*12+4*1)
volume = (/3)
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