What is the surface area produced by rotating #f(x)=1/(x+1), x in [0,3]# around the x-axis?

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Answer 1 · 2016-06-22T08:11:45

#(3 pi)/4#

Desmos

Revolvong a small elemental area about the x axis creates volume of revolution #Delta V = pi y^2 Delta x#

The volume therefore is

#V = pi int_0^3 y^2 \ dx = pi int_0^3 \ 1/(x+1)^2 \ dx#
# = pi [- 1/(x+1)]_0^3 = pi [ 1/(x+1)]_3^0#
#= pi (1 - 1/4) = (3 pi)/4#