Chapter 3 Integration Volume

Chapter 3 Integration Volume Additional Mathematics Form 5

1.

Find the volume of revolution, in terms of, when the area bounded by the curve, the y-axis and the line y=5 is rotated through about the y-axis.

2.

Find the volume generated, in term of , when the region enclosed by the curve, the y-axis and the straight line y=2 is rotated through about the y-axis.

3.

Find the volume generated, in term of , when the region bounded by the curve, the y-axis and the straight line y=3 is rotated through about the y-axis.

4. y

y = x2 + 2

Ox

Find the volume generated in terms of , when the region bounded by the curve,the -axis and = 6 is revolved through 360 about the -axis.

5.

A region is bounded by the curve, the x-axis and the straight line x = -2 and x = -3 . The region is revolved through about the x-axis. Find the volume of generated, in terms of,

[Ans : ]

6.

Find the volume of revolution, in terms of, when the shaded region Q is rotated through about the x-axis.

[Ans : ]

7.

Find the volume of revolution, in terms of, when the region bounded by the curve, and the straight line is rotated through about the y-axis.

[Ans : ]

8.

Find the volume of revolution, in terms of, when the shaded region A is rotated through about the y-axis.

9.

Find the volume of revolution, in terms of, when the region under the curve and the x-axis is rotated through about the x-axis.

10.

Find the volume of revolution, in terms of , when the region bounded by the curve, the x-axis, the y-axis and the straight line x = 2 is revolved through 360 about the x-axis.

[Ans : ]

11.

Find the volume generated, in terms of , when the shaded region B is revolved through 360o about the x-axis.

[Ans : ]

12.

Find the volume of revolution, in terms of , when the region bounded by the curve, the x-axis, the y-axis is revolved through 360 about the x-axis.

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