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Shell method
Setting up the Integral
例题
Example 1:
Example 2:
Example 3:
Example …
个人主页: Aileen_0v0 热门专栏: 华为鸿蒙系统学习|计算机网络|数据结构与算法 个人格言:没有罗马,那就自己创造罗马~ 目录
Shell method
Setting up the Integral
例题
Example 1:
Example 2:
Example 3:
Example 4:
Example 5 :
Example 6:
Practice:
Summary 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 0xpi 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. Example 4:
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. You must include a clearly labeled sketch of the region. Example 5 :
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 x-axis. Example 6:
use the shell method to find the volume of the solid generated by revolving the region bounded by the give curves about the given lines. Practice:
Find the volume of the solid generated by the revolving the region about the given axis. Use the shell method. The region bounded by x3 , −3 1 ℎ 1 Summary
