Answer to Question #220308 in Calculus for Bless

Question #220308
P(2, 3) lies on the curve y=(1/2)x^2+1. O is the origin, M is the foot of the perpendicular to the x-axis and the curve intersects the y-axis at A. The area bounded by AO, OM, MP and the curve PA of the curve is rotated through four right angles about the y-axis. Find the volume of the solid formed, giving your answer as a multiple of π.
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Expert's answer
2021-07-27T14:44:11-0400




y=x22+1y=\dfrac{x^2}{2}+1

V=2π02x(x22+1)dx=2π[x48+x22]20V=2\pi\displaystyle\int_{0}^{2}x(\dfrac{x^2}{2}+1)dx=2\pi\bigg[\dfrac{x^4}{8}+\dfrac{x^2}{2}\bigg]\begin{matrix} 2 \\ 0 \end{matrix}

=8π(units3)=8\pi(units^3)

Answer:8πAnswer:8\pi


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