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Math - Calculus

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Find the volume of the solid given by rotating the region bounded by the curves y=x^2, x=1, x=2, and y=0 around the y-axis

a) Use the shell method

b) Use the washer method. Be careful with the radius of the washer at different y.

  • Math - Calculus - ,

    shells of thickness dx:

    v = ∫[1,2] 2πrh dx
    where r=x and h=y=x^2
    v = ∫[1,2] 2πx*x^2 dx = 15π/2

    washers of thickness dy -- the curved portion plus a cylinder 1 unit high with radii 1 and 2:

    v = 3π + ∫[1,4] π(R^2-r^2) dy = 15π/2
    where R=2 and r=x=√y
    v = ∫[1,4] π(4-y) dy =

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