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Question

Pictured is the graph of the equation 4x²=y(1-y)(2-y)² rotated around the y-axis. Find the volume of the egg. Thank you.

Answer 1

well, clearly we only have to rotate one-half of the curve, and that is

So, using discs, we have

v = ∫[0,1] πr^2 dy
where r=x = 1/2 (2-y)√(y(1-y))
v = ∫[0,1] π/4 (2-y)^2 (y(1-y)) dy
= π/4 ∫[0,1] -y^4+5y^3-8y^2+4y dy = 23π/240

Answer 2

Which function could represent this graph?
a
mc012-3.jpg
b
mc012-4.jpg
c
mc012-2.jpg
d
mc012-5.jpg