solve-the-given-problems-by-integration-the-nose-cone-of-a-rocket-has-the-shape-of-the-solid-that--2

Question

Solve the given problems by integration.
The nose cone of a rocket has the shape of the solid that is generated by revolving the region bounded by $y=\ln x, y=0,$ and $x=9.5$ about the $x$ -axis. Find the volume (in $\mathrm{m}^{3}$ ) of the nose cone. See Fig. 28.12.

Stanley Enemuo · Accepted Answer

The volume generated by the revolver? Um. Uh huh. Why is it good to have you back? What a um accessory. So to calculate the volume, we have to integrate that far back an effervescent airline of X. Squared. But the limits being one and 9.5 again using integration by parts, the answer to all of you. This worldview tv equal to U. V minus the integral of B. D. And we have the volume, The definite answer growth at least 70 17.18.

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.

Carlos Pinilla · Answer

So we have Ah knows corn. He&#x27;s, uh, shape like these gloves up from you, but it&#x27;s, uh it&#x27;s bonded by these curve there. Screwed off eggs for me. Really think so? So that yeah, well, you revolt thes. She are on the sexes thinking something like, Is she doing that? So, uh, we want what it was doing to approximate approximate these Oh, God. If I gaze into two, so dividing that into about, uh So from 1 to 5 point into here with gear like small 21 we want approximated by looking at the ceiling, there&#x27;s inside this shape, so Oh, my God like that. So off them inside the actual few. So, like, these goes wrong, we&#x27;re there until so it is two. With these four shooting this before the last one would have height. Zoo. So that lies. One doesn&#x27;t count. So for each of these similares, we&#x27;re going about with one. So the one is the difference here. That&#x27;s your You know that eggs wacko in the X axis about these one. I&#x27;m here for what? He&#x27;s gonna be there, right? Use So they&#x27;re really use, like for these one. The rain is gonna be at this point, she&#x27;s gonna be the point that for So what for? We have all that point there that raises school before, right? For God, Numbers not scored before. So while the volume here off the ceiling there she go to no bags, he&#x27;s won Thames by thems are they use squared? He&#x27;s being eso these shape it would be Oh, your fix. Thanks. Is you&#x27;re scared of the books on that square would be. Why eggs for? For the city I said we would do. Oh, that volume approximately. Dividing into four. The body more followers. Cylinders would be Look one So bye pins one plus. See you get between two and three. So about releases Screwed to scream. Bloody stool. It was the radius have living three and four within two and three. No, it in two and threes. These one. We&#x27;ve been 300 for Dr Haas. Radius is correct or three. So that square he&#x27;s gonna be free. And then for the last one, it has a radius four. Well, so what did that involve these numbers? These workers, that&#x27;s six plus the four that he&#x27;s seven. But he&#x27;s a tent. Yeah, So these number it would be. Brooks made it by bye, Stan. And they said the number happens to be closed commission by sending a rush remover one point would want.

Adnan Gill · Answer

for the region that we are given is partnered by the line by is equal to two x and X is equal to three. And this point here would be 36 So if we take a elemental piece here, so this is the elemental disk. And if we rotated about the it&#x27;s taxes, then we have a radius which would be equal to why and why is he going to two X and the thickness off? This is DX, so we can now see that E X is equal to pi times R squared or by times two X squared, which would be equal to four pi x quit and the poly would be any crime from 0 to 3. Oh boy Or let&#x27;s see e x dx so that would be equal to in the girl from 0 to 3 ah four pi x quai d x. So what we can do is we can put the four pie in front of the neutral and then goes your 23 x squared the X and we have four pi and the integral off X squared is X cubed over three, and the limits of immigration are from 0 to 3. So we got close four pi and then this would be three to the power 3/3 minus zero. Simplifying. This gives 36 high. Now, if we go back to the Thai Grand, we just read droid here. So what? We are have produced. We have produced a corn essentially and the radius off this corn r is equal to six and thehyperfix each off. This corn is equal to three. So the volume of corn, the formula for volume African is 1/3 pi r squared times each. So that&#x27;s equal to 1/3 pi times six square times three. And when you simplify this, you get 36 pie, which is the same answer we got from immigration.

Tp Sarathy · Answer

All right, so we need to find the sodded off. But the volume of the solid of rotation of this region here, boned by the X axis from the military and the line white will stew. It&#x27;s this line here and align vertical to the problem to the Y direction after the point. Personable basic. That&#x27;s the triangle region. Yes. The region of interest is rotated about. The X axis was really notable. Next sex is and so this is This is the disc problem and the cutest made ah, family to the why, Okay, some distance troponin. Yeah, well, it&#x27;s lander. Okay. And okay. So Ah, that&#x27;s the cut and be rooted about the X of it means this at any given point X here, this distance, the light distances the radius. Oh, this and the assistance. We know it&#x27;s simply the why by coordinate off the line, which means that we can see the, uh, radius radius equal to the y. Coordinate. Okay. And again, keep in mind that the rotating around about the X axis so we shall do, uh, we&#x27;re looking for volume. The integral respect to X is working. Okay, so on him. Okay, so now within the area. We had the radius thrown from about. The radius is away. Quote me So And why is two X so let&#x27;s less With that, the radius equals the Y. Value the sequence, wicks. And so the area is going Bye bye. Are square. It was five times two weeks. What it is now for by ex Quick. Okay, Next we need the volume, which is, you know, is a of Xbox. And this is the record for pie ventricle. X squired the x x in this case, the limits, the X direction. You can see the bone by them. Lower value zero upper values. Three. So it was from 0 to 3. Okay, it is an easy Diggle. And so well, you with this guy comes out to or by the level of X quarters, X cubed by three. And the limits Several three. So when you plug in three, you have Let&#x27;s write off for five C Cube, divided by three is three square. So it&#x27;s nine. Minus again zero. That&#x27;s zero. So that&#x27;s now left it that the six bite is the volume. I&#x27;m Lanza Now we need to very five verify that this is if we had rotated this region about the Mexican. See that? What the solid that gets generated is a coon. And so we need to find Verify that the volume of the corners did this using the standard from low for the world record. Okay, so that&#x27;s still that And the volume of a cone we know is given by you can look up investor toe, go with no textbook or you probably know it. So the volume of a cone, you know, is one or three pi r squared. Thanks, but they had a cone. Whose height? This. Thank you. This is Ah, that&#x27;s a volume. So if your effort of this our region, the radius and height is what we need And so So this is the half the base off. Big stint when the full comb. No. You like fun? The corn, the cones. Highest distance. The radius is this. So the really is&#x27;s is six because he six and the height is the height is okay. Ars six registry The lack in here are the street. So that&#x27;s the square etches six. All right? Oh, actually at it. No, the really is is thick. Yes, it&#x27;s and the height this. And so in the answer Drop park. They looked at six square at 6 36 and they come up with the same and so 36 pipe like we got, right? You using our indignation?

R M · Answer

problem. 45. We have to find the volume on the split obtained by involving the region bounded by one. Why equal to one over square off except a sport on the X axis on the interval zero and it will is removing about why? Why access eso You think she&#x27;ll missile? The volume is equal to five integration from 0 to 12 off X over square root of X IPASS for any X eso the integration for that will be 25 to over three X minus eight square root of X purpose four from Liro, but well, which is equal toe 128 5/3.

Problem

Solve the given problems by integration. The curr…

Problem 40 Easy Difficulty

Solve the given problems by integration.
The nose cone of a rocket has the shape of the solid that is generated by revolving the region bounded by $y=\ln x, y=0,$ and $x=9.5$ about the $x$ -axis. Find the volume (in $\mathrm{m}^{3}$ ) of the nose cone. See Fig. 28.12.

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Basic Technical Mathematics with Calculus

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

Grace H.

Catherine R.

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Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus