Question

Rotate the region bounded by the given curves about the given line and find the volume resulting solid.
x=1+y^2 and the xaxis y=1 to y=2 about the xaxis

Answer 1

\[f(y)=\int\limits\limits_{1}^{2}(1+y^{2})dy=y+\frac{y^3}{3}/_{1}^{2} =(2+\frac{8}{3})-(1+\frac{1}{3})=3.333Unit^{2}\]

Circumference of circle that the rotating shape
diameter = 2
\[Circumference=2\times \pi = 6.28 unit\]

volume = 6.28 Unit × 3.333 unit^2 = 20.93124 unit ^3


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