What is the surface area of the solid created by revolving #f(x)=e^(x^2+x-1)/(x+1)# over #x in [0,1]# around the x-axis?

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Answer 1 · 2017-01-16T01:33:02

# ~~1.45099#

The Volume of Revolution about #Ox# is given by:

# V= int_(x=a)^(x=b) \ pi y^2 \ dx #

So for for this problem:

# V= int_0^1 \ pi (e^(x^2+x-1)/(x+1))^2 \ dx #

There is no elementary anti-derivative. The solution can be found numerically as #~~1.45099#