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Problem 34 Hard Difficulty

Use the result of Exercise 33 to set up an integral to find the area of the surface generated by rotating the curve $ y = \sqrt{x} $ , $ 0 \le x \le 4 $, about the line $ y = 4 $.Then use a $ CAS $ to evaluate the integral.

Answer

$$
80.3034
$$

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Video Transcript

this question asked us to set up an integral to find the area of the surface generated by rotating the curve. Okay, what we know is that we're looking at our bounds from 04 We know we always have to pie outside cause it's a constant you can also write inside, but eventually it will end up being pulled outside. Unless you're using a calculator, then we know we have given the fact that wise four and we have sward of X. We simply have four minus square root of ax, essentially upper minus lower times square root of one plus one over to score of X squared. So you can write the Saudis for Expo Swan over for X is probably easier, because now we're gonna be plugging us into it. Calculator right? It's easier to make it a simplified as possible. And if you could easily square like two squared, it's best to do this before you plug it in. So now if you are to put this directly into your calculator or whatever your online software is math way, for example, you would get 80.30 34