V = ∫ab 2πrh for shells
V = ∫02 2π (9 - x) (8 - x3) dx ...
Josh F.
tutor
That’s the x-coordinate of the pt of intersection between y = x^3 and y = 8.
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02/05/21
Josh F.
tutor
A good graph goes a long way for these volumes of rotation. And it is very useful to draw a representative strip. In this case, a vertical line segment somewhere in between x = 0 and x = 2, between the curve y = x^3 and y = 8, of width dx. Let x = x there and the height and radius of the cylinder should be clear from the graph.
Happy integrating!
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02/05/21
Elle B.
thank you! i was curious you integrated from 0 to 2? where did the 2 come from? thanks in advance :)02/05/21