`2pi int_0^2(y/(1 + y^2))dy` Each integral represents the volume of a solid. Describe the solid.

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The formula `2pi int_a^b yf(y)dy` gives the volume of solid obtained by rotating area under the graph of `f` between `y=a` and `y=b` around x-axis.

Therefore, the solid in question is obtained by rotating area under the graph of function `f(y)=1/(1+y^2)` between `y=0` and `y=2` around x-axis.

Images below show graph of function (blue) and graph of the solid (yellow/orange).

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