The region enclosed by: y= 1/x on the interval (0,∞), x =1 and y =0 is rotated around the x-axis. Consider the generated solid

Question

The region enclosed by: y= 1/x on the interval (0,∞), x =1 and y =0 is rotated around the x-axis. Consider the generated solid. Answer each part below.

a). is the volume finite or infinite? (If finite, find the volume. If infinite, show or explain)

b). is the surface area finite or infinite? (if finite find the surface area. If infinite, show or explain)

If possible please explain the step by step process in a video.

Answer 1

a). Volume v = π∫₀¹1/x²dx = πlim x→0⁺(- 1/x)₀¹ = (- 1 + ∞) = ≈

b) Surface area s = 2π∫₀¹1/x√(1 + 1/x⁴)dx > 2π∫₀¹1/xdx = 2πlim x→0 (ln1 - lnx) = ∞