注意
注意侧面积是旋转面面积，不是表面积
S侧=∫ab2πf(x)⏟周长1+f′2(x)dx⏟弧长 S_{侧} = \int_a^b \underbrace{2\pi f(x)}_{周长} \underbrace{\sqrt{1+f'^2(x)} dx}_{弧长} S侧=∫ab周长2πf(x)弧长1+f′2(x)dx
S侧=∫αβ2πy(t)⏟周长x′2(t)+y′2(t)dt⏟弧长 S_{侧} = \int_\alpha^\beta \underbrace{2\pi y(t)}_{周长} \underbrace{\sqrt{x'^2(t) + y'^2(t)} dt}_{弧长} S侧=∫αβ周长2πy(t)弧长x′2(t)+y′2(t)dt
S侧=∫αβ2πr(θ)sinθ⏟周长r2(θ)+r′2(θ)dθ⏟弧长 S_{侧} = \int_\alpha^\beta \underbrace{2\pi r(\theta)\sin \theta}_{周长} \underbrace{\sqrt{r^2(\theta) + r'^2(\theta)} d\theta}_{弧长} S侧=∫αβ周长2πr(θ)sinθ弧长r2(θ)+r′2(θ)dθ
