Need help with integration of exponential function

Question

The region under the graph y=1/2(e^x +e^-x) and between the lines x=-2 and x=2 is rotated about the x-axis. Find the volume of the solid of revolution formed.

Answer 1

y=1/2(e^x +e^-x)

y^2=1/4(e^2x +e^-2x+2)

Volume of the solid of revolution formed

           b

V= π∫ f^2(x) dx

           a

           2

V= π   ∫ 1/4(e^2x +e^-2x+2)

           -2

                                                 2

     =π/4(e^2x/2-e^-2x/2+2x)

                                                -2

    =π/4((e^4/2-e^-4/2+4)-(e^-4/2-e^4/2-4)

     =π/4(e^4-e^-4+8)

     =π/4(54.6-0.0183+8)

    =π/4(62.582)

   =49.15  cubic units

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I hope that helps u