Question

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

Answer 1

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).