solve-the-given-problems-by-integration-an-electric-insulating-ring-for-a-machine-part-can-be-desc-3

Question

Solve the given problems by integration.
An electric insulating ring for a machine part can be described as the volume generated by revolving the region bounded by $y=x^{2} \sqrt{x^{2}-4, y}=0,$ and $x=2.5 \mathrm{cm}$ about the $y$ -axis. Find the volume (in $\mathrm{cm}^{3}$ ) of material in the ring.

R M · Accepted Answer

problem. 47. Why is equal to sign Inverse X so X is equal to sign. Sign wine. The volume is ableto find from Deal Tau pi over two. Sign Why square de y From the table of the integration, we get that integration off sign squares A X Maniacs is equal to X over two minus sign to a X over four a plus scene. If we make the same opposed, so is equal toe by while over two minus science. So why, over for from zero to fly over to She&#x27;s going to They&#x27;re fine by over four minus sign by over four minor 0/4 plus signed 0/40 is equal to buy squared over.

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.

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.

Sahil Patel · Answer

But here we&#x27;re integrating. Why squared from your tissue animal Playing about hi high times or X squared minus x 1/4. The ex that gives us or ex cued over three. Minus extra fifth over five zero. And I So here we have 32 or three minus 32 or five, which would give us 64 over 15 is 64 or 15 Hi as our final izer.

Tp Sarathy · Answer

therefore, this problem We first need a blot out. Ah, a lot And make it convenient that a two legions given here but two curves that find the boundaries of the region. One other miss why equals refined minus X squared. And the other oneness, Why equals zero? Well, if you want a plots, really forget linguists apartness, Uh, this is let&#x27;s go to the X axis. Why, this girl is why equal to zero outlander and the block this You can actually square this out and see that. So why equals square root off 25 minus x squared? You can square this and to get this and really that and nor the straightaway that this since the equation of a circle with radius better than 25. No, I well, that&#x27;s really when they are, you could just plotted Commended it quickly you plug in the value X equals zero we get why I called square it off 25. So that&#x27;s but I and and then we complain in white on white zero bigot plus five and minus five So we can in ah are out. That&#x27;s the That&#x27;s a region defined by why equals 25 minutes X squared. But this is 20 player minutes X squared. I don&#x27;t and X equals zero. I&#x27;m sorry. Why? But that&#x27;s really the region. Great. So now this is We need to find a wall. Him off the solar There is, uh, generated When this region is rotated with respect to the XX is yes, that&#x27;s the question given. So which means again we need to look for we in terms off bx, which means we will look for the radius will be the area cross section. The radios will be the cut, as you can imagine would be like this direction Which is the why? Why value off off this coat? Yes. Or which means the radius of the media, but not with the radius. So radius radius is equal to the y value. Okay. The Y value which is given by a square root off 25 minus exquisite. Yeah. And so volume is the volume is integral off a off. Why you Why and why is 25 minutes x squared? The or the radius is this You know that the area will be pi Times are square. That&#x27;s by times 25 minus ex quit are. Okay. Um So Okay, that&#x27;s this is this is actually this should be exit. They need We had a drinking water. So So we need until the victim. Okay, we have a already in terms of X, and we need the next Find out where to set up the limits and the X for this region. X extremities are negative. Five and plus, but as we can see, so we plug that in here. Okay, so let&#x27;s go ahead and do this integration place. So that will be people. Negative. 5 to 5. Oh, 25 miners with by 25 minus x squared. B X, which is by times 25 windowless 25 x and interval off X squares X cubed, divided by three. Okay, I just plug in the values now for each or plus five and minus pi. That&#x27;s how you get. Volume is high times 25 times five minus five. Cuba&#x27;s 1 25 divided by three minus. Keep need to be careful with the pluses and minuses this case. So now they&#x27;re back in minus five for this and we get minus 1 25 nine US. Ex Cuban exile minus five is negative 1 25 and so that negative and this NATO will make it. Was it reelected by over three. Okay, and then this is But this is not by times 1 25 minus 1 25 year old by three. And the minus and minus is plus 1 25 and I minus the pluses minus 1 25/3 and you will get a value by times. So they got 2 50 That&#x27;s the is to and then minus this and this would be two times that off $50 but three to give you a final belly off $500 by three times fight. And let&#x27;s verify this. If we have this region like the semicircle like this and the rotator this around X axis, what you would get is a sphere, and that&#x27;s a solid that gets generated. Thank. So let&#x27;s confirm that we know that the volume of a sphere volume of a sphere of radius of radius R is given by oh divided by three times five times radius cube of all the five or are equal to fire. The volume comes out to be four divided by three times by times five Cube, which is 1 25 And so that is exactly what we all right, farmlands of 500.

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Certain algebraic integrals can be transformed in…

Problem 38 Easy Difficulty

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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

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Allyn J. Washington, Richard S. Evans

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