1. CYLINDRICAL DISK METHOD
The region bounded by the curve y = 9-x2, the x-axis, revolved about the x-axis. Find the volume
generated.

2. RING METHOD
Find 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. CYLINDRICAL SHELL METHOD
Find 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]