Originally Posted by

**TKHunny** This is why I like to do ALL such problems both ways. Not only does it provide more practice and more challenging problems, but I get a result verification for free.

WASHERS

$\displaystyle \int_{-\frac{3}{2}}^{1}\pi\cdot\left[(6-2x)^{2}-(4x^{2})^{2}\right]\;dx\;=\;\frac{250\cdot\pi}{3}$

Well, that does support the book. You may wish to recognize that when solving for 'x', there are TWO branches that you might need to consider. Somewhere in that square root, we might need the negative value. Keep your eyes open for it.

SHELLS[1]

$\displaystyle \int_{0}^{4}2\cdot\pi\cdot y\cdot (\sqrt{\frac{y}{4}}-(-\sqrt{\frac{y}{4}}))\;dy$

There's the first piece. What do you get for the rest?

SHELLS[2]

$\displaystyle \int_{4}^{9}2\cdot\pi\cdot y\cdot (What(y)-WhatElse(y))\;dy$