hello i need help on a volume intergration question. (1 Viewer)

bertberk · Feb 12, 2017

q. Find the volume of the solid of revolution formed if the area enclosed between the curves y=x^2 and y= (x-2)^2 is rotated about the x axis.

1729 · Feb 12, 2017

Drongoski · Feb 12, 2017

bertberk said:
q. Find the volume of the solid of revolution formed if the area enclosed between the curves y=x^2 and y= (x-2)^2 is rotated about the x axis.

The 2 curves touch the x-axis at 0 and 2 resp. They intersect at x = 1. By symmetry, the volume of rotation about the x-axis

$= 2 \times \pi \int _0 ^1 (x^2)^2 dx = 2\pi \left [ \frac {x^5}{5}\right ]^1 _0 = \frac {2\pi}{5} $ $ unit^3$

Coincidentally, I was going over precisely this pair of curves a couple of days ago with a student.

hello i need help on a volume intergration question. (1 Viewer)

bertberk

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1729

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Drongoski

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