calculus help
posted by Christine
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
x = 4(square root of (3y)), x = 0, y = 3;
about the yaxis
V=?????

Steve
x=4√(3y)
x^2 = 48y
To use discs, note that the radius of each disc is x, and the thickness is dy, so
v = ∫[0,3] πx^2 dy
= 48π∫[0,3] y dy
= 216π
To use shells, each shell has radius x, and height 3y, so
v = ∫[0,12] 2πx(3y) dx
= 2π∫[0,12] x(3x^2/48) dx
= 216π
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