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\(\displaystyle y = x^3\) , \(\displaystyle y = 8\) and \(\displaystyle x = 0\)

So my question is: Why did they

**cube root**the y (to be more technical why did they put it in terms of x??? I don't understand what this is accomplishing? Can't you just set up your graph and have a horizontal asymptote at

**y = 8**, a parabola that doesn't pass

**(2,8)**, and then just set up your integral and solve as \(\displaystyle 2\pi \int^8_1 x(x^2)\) dx ???

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Nevermind i see what is going on... 2pi * XUse the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x axis...

\(\displaystyle y = x^3\) , \(\displaystyle y = 8\) and \(\displaystyle x = 0\)

So my question is: Why did theycube rootthe y (to be more technical why did they put it in terms of x??? I don't understand what this is accomplishing? Can't you just set up your graph and have a horizontal asymptote aty = 8, a parabola that doesn't pass(2,8), and then just set up your integral and solve as \(\displaystyle 2\pi \int^8_1 x(x^2)\) dx ???

so thats why you set x =