Home/Calculus II/Applications of the integral/Surface of revolutionSection 10.6Surface of revolutionAround the xxx-axis, with f(x)≥0f(x)\ge0f(x)≥0:Copy LaTeXS=2π∫abf(x)1+[f′(x)]2 dx.S=2\pi\int_a^b f(x)\sqrt{1+[f'(x)]^2}\,dx.S=2π∫abf(x)1+[f′(x)]2dx.View detail →Around the yyy-axis, with x≥0x\ge0x≥0:Copy LaTeXS=2π∫abx1+[f′(x)]2 dx.S=2\pi\int_a^b x\sqrt{1+[f'(x)]^2}\,dx.S=2π∫abx1+[f′(x)]2dx.View detail →For another axis, the radial factor must be the distance to that axis.
Around the xxx-axis, with f(x)≥0f(x)\ge0f(x)≥0:Copy LaTeXS=2π∫abf(x)1+[f′(x)]2 dx.S=2\pi\int_a^b f(x)\sqrt{1+[f'(x)]^2}\,dx.S=2π∫abf(x)1+[f′(x)]2dx.View detail →
Around the yyy-axis, with x≥0x\ge0x≥0:Copy LaTeXS=2π∫abx1+[f′(x)]2 dx.S=2\pi\int_a^b x\sqrt{1+[f'(x)]^2}\,dx.S=2π∫abx1+[f′(x)]2dx.View detail →