一道英文的微积分题Find the volume of the solid that is obtained by ro

来源：学生作业帮编辑：作业帮分类：英语作业时间：2024/05/15 15:17:54

一道英文的微积分题
Find the volume of the solid that is obtained by rotating the region bounded by the curves y = sec x,
y = 1,and the lines x = -1,x = 1 about the x-axis.

Using the disk/washer method,we generate washers upon roating the region about the x-axis.
The bigger radius is sec x - 0 = sec x.
The smaller radius (for the hole) is 1 - 0 = 1.
So,the volume equals
∫(x = -1 to 1) [π(sec x)² - π * 1²] dx
= π ∫(x = -1 to 1) (sec²(x) - 1) dx
= 2π ∫(x = 0 to 1) (sec²(x) - 1) dx,since the integrand is even
= 2π (tan x - x) {for x = 0 to 1}
= 2π (π/4 - 1).
再问： http://zhidao.baidu.com/question/1754126934588571548.html 可以把这道题也看看嘛？谢谢你了！

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