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# Volume of curves revolved about an axis using integration

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### Volume of curves revolved about an axis using integration

1. 1. CYLINDRICAL DISK METHODThe region bounded by the curve y = 9-x2, the x-axis, revolved about the x-axis. Find the volumegenerated.
2. 2. RING METHODFind the volume of the solid generated by revolving about the x-axis the region bounded by the curves y= x2 and y = -x2 + 4x.
3. 3. CYLINDRICAL SHELL METHODFind the volume of the solid generated by revolving about the y-axis the region bounded by the curves y= x2 and y = -x2 + 4x.Seatwork: 1. Find the area bounded by the line x – 2y + 10 = 0, the x-axis and x=10. [Ans. 100 sq. units] 2. Find the area bounded by the curve y = x3 + 3x2, from x=0 to x=2. [Ans. 12 sq. units] 3. Find the area bounded by the curve y = x1/2; from x=1 to x=16. [Ans. 84 sq. units] 4. Find the area of the region bounded by the curve y = x 2 – 4x, the x-axis and the lines x=1 and x=3. [Ans. 22/3 sq. units] 5. Find the area of the region bounded by the curve y=x3 – 2x2 – 5x + 6, the x-axis and the lines x=-1 and x=2. [Ans. 157/2 sq. units] 6. Find the volume of the solid revolution generated when the region bounded by the curve y=x2, the x-axis and the lines x=1 and x=2 is revolved about the x-axis. [Ans. 31π/5 cubic units] 7. Find the volume of the solid generated by revolving about the x-axis the region bounded by the parabola y=x2+1 and the line y=x+3. [Ans. 117π/5 cubic units]