Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.3 Area of a Surface of Revolution, #21 · Calculus · Applications of integrals

Explain why the surface area is infinite when … is rotated around…

Explain why the surface area is infinite when $y = 1/ x$ is rotated around the $x$ axis ( $1 ⩽ x < \infty$ ). But the volume of "Gabriel's horn" is ____ . It can't enough paint to paint its surface.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.3 Area of a Surface of Revolution, #21

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