solve-the-given-problems-by-integrationan-architect-designs-a-wall-panel-that-can-be-described-as-th

Name: solve the given problems by integrationan architect designs a wall panel that can be described as th
Uploaded: 2020-06-19
Duration: 6 min 19 s
Channel: Numerade
Description: Solve the given problems by integration.An architect designs a wall panel that can be described as the firstquadrant area bounded by $y=\frac{50}{x^{2}+20}$ and $x=3.00 .$ If the area of the panel is $6.61 \mathrm{m}^{2}$, find the $x$ -coordinate (in $\mathrm{m}$ ) of the centroid of the panel.

Question

Solve the given problems by integration.An architect designs a wall panel that can be described as the firstquadrant area bounded by $y=\frac{50}{x^{2}+20}$ and $x=3.00 .$ If the area of the panel is $6.61 \mathrm{m}^{2}$, find the $x$ -coordinate (in $\mathrm{m}$ ) of the centroid of the panel.

Robert Daugherty · Accepted Answer

Section 76. Problem number 44. So here I am asked to find the area between a curve which you see given here, one over the square root of X square monies to X plus two area between that curve, the X axis when x goes from 0 to 3. So let&#x27;s take a look at it first. So what you see here is the graph of the the initial curve. What you see here, I&#x27;ve got X goes from zero 23 And so I&#x27;m being asked to find this shaded area, which means, basically, I need to find the integral from 0 to 3 for this function, and it turns out to be about 2.3 to 5. So I&#x27;m gonna get an exact value, and it&#x27;s approximation should be very close to ah, that number. So, in this case, what I&#x27;m doing, I&#x27;m using, um, integral look up tables. And so let&#x27;s just take a look. I&#x27;ve been using the table that you see here that referenced, um, and so I go and I look one up and this is illustrates. You got a sort of be on top of your game here. There&#x27;s a typo in this particular problem. So you see this Actually, what this one is is this is the integral of the one that I&#x27;m looking for One over a x weird plus b x plus c d x. They forgot to put the square root sign. And this works when a is greater than zero. So this is actually what I&#x27;m looking forward. So all the key reason that you&#x27;re gonna have to really know how to integrate you can&#x27;t rely always on integral table toe work it for you. So let&#x27;s go back and let&#x27;s just write down What? That solution Ah, would be, um so according to our interval look up table, I know that the indefinite integral one over square root X squared plus B x plus See the X is going to be equal to one over the square root of a natural log to a X plus B plus two square root of a and in the square root of a X squared plus BX plus c And then all of this, plus a constant. And this is when a is greater than zero. So in my case, I need to do this particular problem where a coefficient of the quadratic term is one be coefficient of the linear term is negative. Two. And see the constant term is positive, too, so I would need to substitute those values in. So just using this formula, you&#x27;ll have one over the square root of one natural log two times one times acts plus negative, too, plus two times one, um, and then the square root of X squared, minus two X plus two. And then all of this is evaluated from 0 to 3. So let&#x27;s clean this up just a little bit. This is the natural log of two X minus two plus two square root of X squared on its two X plus two. Evaluate from 0 to 3. So let&#x27;s do this evaluation. Calculus is over. We&#x27;re into arithmetic now, so substituted three into that expression so you&#x27;ll have the natural log. And when you substitute a three, you have six minus two plus two. You substituted three. You&#x27;re gonna X square. That&#x27;s 99 minus six is 33 plus two is five that when you substitute a zero, you&#x27;ll have natural log zero minus two plus two, and then the square root of to. So what we have now we&#x27;ve got the natural log of four plus two, Route five minus the natural log. And I&#x27;ve got to root two minus two. If I put all of these together, this is the natural log four plus two, Route five divided by 22 minus two. In fact, or two out of the numerator and denominator, You&#x27;re gonna get to two plus Route five over to, um Tu minus one. These 2/2. That&#x27;s going to be one. So this final answer is going to be the natural log two, plus Route five over route to minus one. Substitute that into your calculator. That is about 2.32 50 And then how does that compare? You see, 2.3 to 50 So we were correct in making that work. So again, the key here Waas. I needed to graph it to actually see what&#x27;s happening between zero and three to tell me that the integration will indeed find the area under the curve. Then I write down this integral and I go to my integral table. And in this case, there was an error in my integral tables and hopefully years will not have that. Um, correct that Arab used the formula substitute, do the arithmetic and get down to the final answer here.

Khoobchandra Agrawal · Answer

Hello Everyone be approved. Fight sent right off the city area sent, right? Oh, the city area. The 80 IES given absolute That figure This is my exit. It&#x27;s the act sexist. This is the party. This better is given one meter. It&#x27;s equally Senate by Scotto I went by e x squared So this better you are not known to us that we required to calculate for acts will be but maker. Bye baby. Why fight it&#x27;ll deep our one that is but quite 259 meter. So this is your three point 11359 meters or here, you know by is given Why fight into the power X? This is your first depression People considered elemental area this off to be X on having departed it X and bite So area off element D A ruby from here you can t area will be This leg will be total is this and this is by so this will be 1.35 night minus eight and gx and having sent right having sent right eggs coma one plus 35 night minus by divided by two So central x off the serial area would be eggs in tow. Be upon integration off the for the limit. You don&#x27;t know, but no hay here, you know 1.35 night minus why and d x 1.35 night minus bite. B X are here. It would be X here. I make a correction. This I have written wrongly. So this is here is right. No value off by vino substituted. Here we will get Sen droid X off Proceeded area would be Joe Tobin meter, but white 359 minus by. And why haven&#x27;t they? Why buy X squared and do X dx Do I do to bite 1135 night minus. Why fight e to the power X squared you get no indeed. Break numerator and innovator and substitute the limit. Then ST Droid X, you will get That is white 398 meter. This is the answer for this problem. Thanks for watching it

Khoobchandra Agrawal · Answer

this. Hi, everyone. We have to locate the same tried bite off the said your person. You are sited idea as given in the diagram. Let us hear the Bagram. This is XX. It waxes. This is the origin here. The question is by skull toe. Why fight explosions off excess sweat? I This is one meter, so it is given by skull toe. Why buy exponential off excess where this value had not given? We can calculate for access Cult over by Willoughby. Why fight e one guy&#x27;s square? So this will be one point 359 meter. So this is one point 359 meter. Not we will consider any elemental area. This is your elemental area. Uh, averted. DX on It&#x27;s coordinates are X and bite. See that again? So this is what so elemental area be a bility This link One point this land be required. So totality, 1.35 night minus bite into the X. Having send droid at this elemental area having the same troy at eggs plus 1.3 books. Five nights. But let&#x27;s buy divided by two. So ST, right, right off stated idiom. You mean right but wind 359 plus by divided by two day eight upon integration off, do you no Substitute the value here one climbed 35 night, but less by in tow. D 88. We have rated minus bite be x 1.359 Miners bite DX. A limit is 0 to 1 meter so we can write center Vital be judo group one. Here it is, half substitute the value of white. Yeah, be after substitute the value of by so you can write one plus 359 Who knows? White five feet deep. Our X in tow. 1.359 minus point Fight into explanation Are pecs DX divided? Right? 11359 minus point by exponential Affects Deitz When you solve a new military, it would be how in digressing from 0 to 1, you may be right. 1.847 minus wind proof fight explanation Off to exit square be X Do I did by 1.35 night minus. Why fight it to the power excess sweat? No, we have to use the help for us to integrate numerator and denominator and on solving it The central oId You will get one meter. So this is that Everybody off integration so that I&#x27;m not going to risk associate. I&#x27;m directly writing. Answer. Your final region will be sent right at me.

R M · Answer

took them a number 44. The volume is given by the formula B is ableto by integration from one to eat off X square square off learn x all squared D X, which is equal to far immigration from Want we off export four, then x at the X, which is equal toe X for four plus one. Learn X over four plus one minus 1/4 plus one squared substitution from me from me toe one, which is equal toe he 45 1/5 minus 1/25 minus zero, minus 1/25 which is equal to four or five plus one over 25.

Doruk Isik · Answer

in this problem, whereas to find be central mess off the shape formed by the line wise, you could do X lines y zero and X equals. One said that it would be to shape this shaded region and usually it looks like central Mass should be somewhere around here. Now, mathematically and articulate, less calculated. We first need to find the area off that shape and less first, then find the limits off integral. Since we&#x27;re gonna take 10 strips with with DX and now we&#x27;re going to some goes up, Um, we go from X equals zero X equals well, sort of limits. Infringe uncle would be 0 to 1. We have the function to x times DX that would be ex crab, where X goes from 0 to 1 in the area with them Meet one. You know that export is you go to one over area internal from a to B, where we know it to be 01 x times ffx d x What is several? Thanks. Well, this is our f effects wise equal to x. So we have one over one in general from 0 to 1 x times two x The eggs that is equal to two times X cube or three words changes between zero and one, so we can see that export is an equal to two over three. Well, for why bar we have are integral as one or area from A to B, where a zero bees won&#x27;t we have one? How off the function squared the eggs that is areas one. So we have interviewed from 0 to 11 health. It affects his two acts. F of X court is four X squared D eggs that is then equal to these will cancel out He had two X cube over three or exchanges between your on one. And from this we see that why bar is all security. So the center of mess off the system list too earthy and two over three

Problem

Solve the given problems by integration.The power…

Problem 49 Easy Difficulty

Solve the given problems by integration.An architect designs a wall panel that can be described as the firstquadrant area bounded by $y=\frac{50}{x^{2}+20}$ and $x=3.00 .$ If the area of the panel is $6.61 \mathrm{m}^{2}$, find the $x$ -coordinate (in $\mathrm{m}$ ) of the centroid of the panel.

Answer

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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