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calculus 2

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find the volume of the solid obtained by revolving the region bounded by the graphs of y=2+4x-x^2 and y=2 about the line y=2.

  • calculus 2 -

    y-2=4x-x^2
    The volume=pi*Int.[0,4](4x-x^2)^2dx=
    pi*Int.[0,4](16x^2-8x^3+x^4)dx=
    pi*(16/3x^3-2x^4+1/5x^5)[0,4]=
    pi*(1024/3-512+1024/5)=pi*1024/30

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