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# The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.$y^2 - x^2 = 1$ , $y = 2$ ; about the x-axis

## $V=4 \sqrt{3} \pi$

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Applications of Integration

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The problem is the region bounded by the Cuban curves is rotated about. This classified access find is a volume of the resulting salad. I mean, my third. First we can sketch this region. This's a curve. Why squire minus x square. Could you one This line is why to two on dirt. This point is one. The region is thiss part. We need to rotate this region about X axis with this problem first, that we can compute the warrior A tiny bite rotated, pretending this part about X axis and then multiply two is the volume over time the bio tidying the whole ours. Here we use my third of cylindrical shells. So the is a culture too high going to grow from one to two. Why times for you to know why have y square months x square you could want So Max is the co two. Why square ones? One which if this one This is Max here why my fly? Beautiful. Why square minus one? The what? And then multiply too. Think thiss part is the volume attaching half earth this region about X axis. This's a cultural or pi ham's inter girl from one to two. Why would it if y squared minus y minus one t? Why here? We use you substitution at you. Is he culture? Why square minus one then? Do you want to know why you want this's equal to two high Integral from zero two three Andi, you to half you. This is because you're too pie. Times two over three. You two three over too. Ground zero to three. Arthur, it is too high. Arms to our three times, three years. Three. This's the unconscionable. Four times you two, three times.

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