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(3) x = 1 的极坐标方程是 rcost = 1，即 r = sect
原积分化为极坐标
I = ∫<-π/4, π/4>dt ∫<0, sect> √{r^2[(cost)^2-(sint)^2]} rdr
= ∫<-π/4, π/4>dt ∫<0, sect>√[(cost)^2-(sint)^2] r^2dr
= (1/3)∫<-π/4, π/4>√[(cost)^2-(sint)^2](sect)^3dt
= (1/3)∫<-π/4, π/4>√[1-(tant)^2]dtant = (1/3)∫<-1, 1>√(1-u^2)du
= (1/3)(π/2) = π/6
原积分化为极坐标
I = ∫<-π/4, π/4>dt ∫<0, sect> √{r^2[(cost)^2-(sint)^2]} rdr
= ∫<-π/4, π/4>dt ∫<0, sect>√[(cost)^2-(sint)^2] r^2dr
= (1/3)∫<-π/4, π/4>√[(cost)^2-(sint)^2](sect)^3dt
= (1/3)∫<-π/4, π/4>√[1-(tant)^2]dtant = (1/3)∫<-1, 1>√(1-u^2)du
= (1/3)(π/2) = π/6
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