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目录
Shell method
Setting up the Integral
例题
Example 1:
Example 2:
Example 3:
Computing volumes for solids of revolution using cylindrical shells（利用柱壳法计算旋转体体积）:
Shell method
柱壳法对于旋转固体体积的计算公式如下：
Setting up the Integral
• Keypoints:
1. When using cylindrical shells, you integrate with respect to the variable that is perpendicular to the axis of rotation.(使用柱壳法时，可以相对于垂直于旋转轴的变量进行积分)
2. The integral can be set up as 2π ∫(a to b) r(x) h(x) dx or 2π ∫(c to d) r(y) h(y) dy , depending on the orientation.
例题
Example 1:
Use the shell method to find the volume of the solid generated by revolving the shaded region about the y-axis.
Limit is 0<x<pi
Example 2:
Use the shell method to find the volume of the solid generated by revolving the shaded region about the x-axis.
Example 3:
Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis.
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