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Problem 18 Medium Difficulty

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis.

$ y = \sqrt{x} $ , $ x = 2y $ ; about $ x = 5 $

Answer

$V=\frac{136 \pi}{15}$

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hd

Hoang D.

April 23, 2020

fuck you

Video Transcript

given the fact we're gonna be slicing this way. We know the radius is five minutes, max and the height escort of ex my specs over to, which means our volume is two pi times into girl from 04 radius times height, de vex. So get five months acts, time squirt of acts minus X over too. D x, Which means now we can simplify this before we interest. Let's simplify. Okay? Integrate. Which means increased the exponent by one divide by the new exponents. A lot of stuff is gonna be canceling off, as you can probably see, because it's like when we multiply by six and then divide by six, we just end up with one. So that's why a lot of stuff cancels off now at the point where we can plug in our two bounds for an zero. When we plug in zero, we actually just end up with zero. So that doesn't matter in this context, because those ear doesn't affect the problem. Like I said, this is minus zero, which we can ignore. We got 1 36 pi divided by 15