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# The region between the curve $y=1 / x^{2}$ and the $x$ -axis from$x=1 / 2$ to $x=2$ is revolved about the $y$ -axis to generate a solid.Find the volume of the solid.

## 4$\pi \ln 2$

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in this problem, whereas funny oh, opera region between why or function? Why? When x spread. The XX is where exchanges for one off too. So let's first applauded and see what's going on. So this is our home. She won. This is why I wantto ex great. This is our excesses. Um, it let's say that this is X or help on Dennis's face too. So we have this region here and we own bowling this. Why exits suck it be Do so As you can see, there's another region, right or active, this one. And if he were terrible this shaded regions around, why axes? We would get an empty region right here if you would get a whole right. Since we are getting an A hole, uh, we're gonna use the shell meant it. So it tells us that one of you is equal to the lower bound the upper bound to pine x times our bags were Our function is for over ext Sprite. Now integrate this over ends. No, Ben are buoyant function ear's on how to to pine eggs or cancel out to pine times ward off X v X two pies just a constant. We know not integral. One of X t x is natural law off X four exchanges between one health and to let's find it. Morning, Liz, than equal to pine natural law off too. Minus natural, lago. One health using properties off. Ah, Lorraine Burch is this is too five times natural law to over one hell. Um, that is equal to two high. Next lot off full. Wherefore is two squared. So there we can find evolving to be or high natural law off too. What you did that is that we take this power off too, and put it here as the most choir. That's how we got this for.

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