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Problem 2(4 points) Let R be the region bounded by y = Vx and y = x for 0 < x < 1. Find the volume of the solid obtained by rotating the region R around the y...

Question

Problem 2(4 points) Let R be the region bounded by y = Vx and y = x for 0 < x < 1. Find the volume of the solid obtained by rotating the region R around the y-axis_Volume is

Problem 2 (4 points) Let R be the region bounded by y = Vx and y = x for 0 < x < 1. Find the volume of the solid obtained by rotating the region R around the y-axis_ Volume is



Answers

Concern the region bounded by $y=x^{2}$, $y=1,$ and the $y$ -axis, for $x \geq 0 .$ Find the volume of the solid. The solid obtained by rotating the region about the line $y=-2$

The question given us from the topic. Electronic confirmation and predictable. And this question is out there Some of the data on the numbers could not explain why. So basically there are three sets of data given to us and that which only holding cannot why this cannot occur. What's the reason the first one other data set given us and equals two. L. Equals one Emily close two and everything was. That's not. So for solving all the question in fact there's somebody that we must know. The logic is he doesn't point that will never that will always be checked and can never be caldwell. First point they can, point value is always from 02 in -1 cannot go beyond it. I love animals. They're always be minus L. Two plus and it cannot go more than that and develop M. S. Is always either a positive value positive or a negative. Have it cannot be something else. Using this will be able to answer all the questions. Let's look at the first one here and it's fine. It's also fine. But ml cannot be more than L value. It has to be from minus 20 minus two plus, meaning minus one to plus one plus two. So here I am. L is not in order, it's not incorrect format and well it's not proper value is not proper because can only be from minus 12 plus one. B. Big question is saying three and these three Ls two, you know, is zero and mrs minus off here and in in and then it's not in the sense that would be correct. Even the whole hellos from between minus group zero And so the plus two. That's also correct. This is correct. So this is this data. Okay. The unit is correct because it has all the rules followed this, not the Improper one or it will occur third one and it was one L equals zero. Emily equals zero in this one. This can never be true because of two reasons. The first reason only isn't particularly and this cannot be what? Because it has to be either. I then minus about this will not exist. So it cannot offer could no longer what can a doctor? That's what we can. Right in this question. It cannot occur In the one. The last one it is N equals two. L equals zero. M. L zero and this that's half. So here is clearly see that the unity is cut because it's all the rules are followed. Therefore this will occur because it is totally correct. So I wouldn't question the first data is kind of parent because it has all the because it is not proper before it don't exist. It will not occur because Emily is not proper And it should be -1 to between that value. The data. Spirits. It will you. It occurs third one Port one cannot. So these are the answers for the question, so the answer for the first one, His Emily is not proper. It won't take place. 2nd 1 is the latest correct. It will take place since here it is not current, it won't the last one. This will occur because that it is properly given.

The communications on the topic. Electronic conversion and predictable. This question is asked. That assign correct set of 400 numbers for each territory in a referendum electronic sodium atoms and three electron in a nickel atom. So basically we have to do there were many continents of the following. So let's start selling this question. So first a part the convention is for nitrogen, nitrogen is seven. The convention will be one is two. Two ways to goofy thing is the competition right there. It turns here. This is the contribution. One is one in one is two. That to us too. And this is took me three. So that is an idea that only communication for each of the act Children are done here with this. The confession would be N equals one. L. Equals zero. Emily equals zero. And this would be do it for me. That's how but this one and equals to one and it was zero first. Still the same because they belong to the same in the middle. This will be our worried because the police present principles. The fourth orbiter 1st 1st 4th 1 must be exclusive hear any cost to to because there's belonging to second shelf as you can see that would be zero even though as well my name is will be positive because it is a brand here. But this electron this is for this electron but the other one anything was to do L zero. Let me show it properly. This one is from this one and this is for this one. Mm would be zero as well. My name is would be minus and where these electrons the confession will go somewhere for this one. This one and there's one. The conversation would go something like this. Well this particular item, the competition will be and it was two. It was extremely thick himself. L equals one because it's the orbital this would be minus 10 plus one. I got an animal like this. So for this electron here it will be plus one. And MSs operates a little weak person here for this middle tone and it's too LS one Emily's one as well. But this would be Yeah, you see everything is somebody here. B zero, not 10 Okay, the last one. And as it goes to and he goes to one and then it goes through minus one. This is a question. This is the computation. We can write for nitrogen all directions, moving on, moving on to the next part of the thing. The internet, tons of sorting. This is a big part. So did the electronic confirmation of sodium sodium is one is to to us too, to physics three years one. So this is this is the valence electron that we have. This is the and we have so let us all the contribution to the conversation. This one. The end would be t there will be zero mm will be you know as well. This would be plus because it just operates. The question. The question is the 31 of the electron in Nicoletta. What is the confession Nicole Nicholas 20 7 28. The contribution is want us to to us too, statistics increase to three P six for us to really it. So we can write they're asking for one electronically they can rather date configuration. Then you can choose to write any one of the they're turning configuration. So let's do it one. This is training. So 1234 Why 678? You can ask for anyone. Let me write it for this electron again. Right. For any other one as well, the end will be three because there's 3/2. L. Would be too because in the er and it would be I can choose minus two minus 1012 loaded as zero because it's in the middle one and a middle M. S. Would be minus A. Because it is the downward pointing electoral. These are the electronic contribution for the asked to return in this question for me is that the answers? So for me the answers are all of these quantum numbers or B. The answer is his condone imus. And foreseeing the answer. In these controllers deserve the answers only from one question.

Girls given to us Old boy equal one minus X squared power over Negative, huh? And war equal four We had what boy? Equal one minus X squared bone negative one and Roy equal four intersects ed plus or minus square root 15/16. Therefore X raise from minus square root 15 over 16 to x equal square root. 15 over 16 Since our girl war equal one minus X squared or negative half which is containers and also the care. If off X is bigger than or or equals zero in the given region, so will you quit integration e be boy every fix square the X Equal boy Integration square root 15/16 minus square root 15 over 16 Poor squared, minus one over square root, one minus X squared over two d x Equally boy integration square root 15 over 16 minus square Root your hangover, Dean thing minus one over one minus X square The X Equal boy Phoenix minus 1/2. Lynn one plus X over one minus x, but would square picks. It's equally it. Boy square root 15 minus. Oh boy, Lynn four plus Square Root 15. This will be the final inst

In the question we have to find the volume of a solid obtained by rotating about by excess. And the region bounded by the curves by school. Three to the power minus x square by schools to zero X is close to zero and excess calls to one. Now moving towards the solution here, rotating about the y axis. The cylindrical shell method will be simpler. So like the height equal to E. To the power minus X. Two minus x square. So the radius will be equal to R. S equals two weeks which goes from 0 to 1. So we will be equal to integral of two by R H. D. X. That is we will be called to to buy into integration from 0 to 1 X into E. To the power minus X square D. X. Now we will be solving this integral. So let you be equal to minus x square and then do you will be equal to minus two X. Dx. That is minus one by two D. You will be equal to x dx. So putting these values you will get your limit going from a equals two minus x square to minus zero square that is zero and we will be from minus one square that is minus. But so the integral will be Dubai into Integration from 0 to -1 -1 by two E. To the power you do you Solving This? You will get -9 E to the power you limit going from 0 to -1. That is minus phi into each of the power minus one minus one. Solving this. You will get your answer approximately equal to 1.986 Thank you.


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