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Solution assignment 09 Area and volume

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Assignment 9

Calculate the volume of the paraboloid which is the result of revolving the parabola y=x^2+1, y\in[1,3] around the Y-axis.

Solution

From y=x^2+1 we get x^2=y-1 and we use the formula:

\displaystyle\int_{1}^{3}\pi{x^2}dy=\int_{1}^{3}\pi(y-1)dy=

\displaystyle=\pi[\frac{1}{2}y^2-y]_{1}^{3}=2\pi

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