Calc 2

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Find the area of the surface generated when y=4x and x=1 is revolved about the y-axis.

  • Calc 2 -

    No calculus need for this one. It's just a cylinder with a cone cut out.

    r=1
    h=4

    v = πr^2h - π/3 r^2h = 2π/3 r^2h = 8π/3

    Ok ok. If you want to use calculus, then with shells,

    v = ∫[0,1] 2πrh dx
    where r=x and h=y=4x
    v = ∫[0,1] 2πx*4x dx = 8π/3

    using discs (washers) you get

    v = ∫[0,4] π(R^2-r^2) dy
    where R=1 and r=x=y/4
    ∫[0,4] π(1-y^2/16) dy = 8π/3

  • Calc 2 -

    We have to use the Surface area of revolution formula

    integral(f(x) aqrt(1+f'(x)^2))

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