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Problem 9 Medium Difficulty

Use 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.

$ xy = 1 $ , $ x = 0 $ , $ y = 1 $ , $ y = 3 $

Answer

4$\pi$

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Video Transcript

Okay, The first thing we know is that we have a d. Y interrupt because they've said use Linda ical shells and surround the X axis. So this means that if acts why is one than acts solved is equivalent to one divided by what? Now we know we're gonna be integrating from 1 to 3. We know ours. Why? And height is equivalent to X, which we just established is one over. Why again? Because of the nature of the fact that we're using cylindrical shells and the way we are rotating. Like I said, this is all gonna be in terms of why that's why it's do you why this is really important for this problem over here. So plug in our bounds putting the information I just said, Why times one over. Why do you why Okay, we can simplify this to pie times integral from 1 to 3 of literally just one d y. This is a pretty straightforward integral. This simply to pi times y from 123 and to grow of one is simply why If it was, if it was in terms of X, it would've been X just in terms of why, For this one plug in our bounds and we end up with four pi is our solution