5

(1 point) Assume € 0 and A > 0,and compute the volume of the solid obtained by revolving the region bound by the graph of f(x) = Axo.5 , the vertical line ...

Question

(1 point) Assume € 0 and A > 0,and compute the volume of the solid obtained by revolving the region bound by the graph of f(x) = Axo.5 , the vertical line X = C, and the X-axis about the X-axis. Your answer should be in terms of A and c_VolumeHint: Use the method of washers or discs

(1 point) Assume € 0 and A > 0,and compute the volume of the solid obtained by revolving the region bound by the graph of f(x) = Axo.5 , the vertical line X = C, and the X-axis about the X-axis. Your answer should be in terms of A and c_ Volume Hint: Use the method of washers or discs



Answers

$1-18$ Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.
$y=\frac{1}{4} x^{2}, x=2, y=0 ;$ about the $y$ -axis

Were given a set of curves in the line and were asked to find the volume of solid obtained rotating the region founded by these curves about this line. Curves are X equals thes squared X equals one minus B squared. The line is X equals three. Yeah, so mhm al draw first, the graph of the region. Now it's actually easiest to do this by drawing the curves separately first. Now the draw X equals the square. This is simply a parabola opening upwards. So the graph X equals V squared. This is simply a parable on its side. This points of the origin also at 11 to graph X equals one minus B squared. This is also a Prabal on its side. It's facing towards the left, has an X intercept of one. It also has points at zero plus or minus one. And so it's easy to see that this region here in red is the region that we're interested and rotating. And the points of intersection by symmetry are going to be at X equals one half. And so this is one half and then plus or minus 1/4 and we went to rotate about the line. X equals three. We're sorry, not 1/4 but this should be plus or minus one of the route to So did your all the solid would really only need the 1st and 4th quadrants. And here I make the scales a little bit different for clarity. And so we get a solid that looks something like this being irritated and typical cross section of this solid, He's going to look like this. Looking at the cross section, we see that it is a washer which has an inner radius, which is the top, which is three minus the bottom function, which is one minus X squared. This is two plus X squared and has an outer radius, which is the top three minus the bottom function, which is X equals V squared. Sorry. Should be one minus b squared. And so the area of this washer is pi times three minus V squared, squared minus pi times two plus v squared squared, which simplifies two pi times nine minus six v squared plus feet of the fourth minus four plus four v squared plus feet of the fourth. So we get pi times five minus 10 V squared. Therefore, the volume of this solid it's going to be the integral from three equals negative. One of the route to to V equals positive one of the route to of the area of the washer. So this is the integral from negative one of the route to to positive one of the route to of pi times five minus 10 v squared Devi Function in the instagram is even so This is equal to two pi times the integral from 0 to 1 of her too of five minus 10 v squared d v By symmetry and taking anti derivatives, we get two pi times five v minus 13th V cute from 0 to 1/2 and substituting values. We get two pi times five of a route to minus 10 thirds times 1/2 or two or 5/3 route to miss simplifies to 10 pie times route to over three and so our answer is 13th route to pie

Were given a set of curves in the line and were asked to find the volume of the solid obtained by rotating the region. Bounded by these curves about this line curves or why equals X Cubed y equals X and X is greater than or equal to zero. The line is about the X axis first straw, the region in the X Y plane that will be rotating. So this is going to be in the first quadrant. So why equals X cubed as points at 00 11? Michael's ex also has points there, so really focusing just on this one small region. Where is y equals? X Cute has a value of 1/8 at one half. Why equals X is the value of one half one half. And so this region in red is the region that we're going to be rotating about the X axis. In order to do this, I'll draw a second graf, which contains the 1st and 4th quadrants. So we get shape that looks something like this. So this is the solid. And if we take a cross section of this solid, we see that it's in fact going to be a washer. It looks something like this. So looking at graph of our solid a cross section is a washer or analysts, inner radius X cubed and an outer radius of X. Therefore, the area of the washer, The FX is pi times X squared minus pi times x cubed squared which is the same His pi times X squared minus six to the sixth in the volume of this solid is the integral from X equals zero to x equals one of the area DX, which is the integral from 01 of pi times X squared minus X to the sixth, the X taking into derivatives This is pi Times one third x cubed minus 1/7 extra seventh from 01 Substituting This is pie times one third minus 17 which simplifies 24 20 firsts times pi

Were given a set of curves and a line were asked to find the volume of the solid obtained by rotating the region bounded by these curves about this line were also asked to sketch the region's solid in a typical disk or washer. The curves are why equals one minus X squared. Why equals zero and the line is about the X axis. So the simplest thing to do first is to draw the region and then the solid. So for drawing region, this is going to be upside down parabola. So in the 1st and 4th, 1st and 2nd quadrant, sir, is where we're really concerned. Here it has intercepted X equals plus or minus one in his Y intercept and one So we have a shape like this, and then also y equals zero with this horizontal line. So this shape and red is our region that we're going to rotate about the X axis. So I'll do this over here and here. We're going to use all four quadrants may rotate this the roughly, get a picture like this. So we've got our parabola and we have that It gets mirrored across the bottom and a typical slice of this solid is going to be a disk looks something like this from our pictures. It's clear that a cross section is a disk with radius one minus X squared. In the area of this disc is at X, which is going to be pi times one minus x squared squared. Therefore, the volume of the solid the is the integral from X equals negative 12 positive one of the area DX, which is the integral from negative one deposit of one of pi times one minus X squared squared DX, which can be simplified by noticing first of all, that the function in the instagram is even so weaken double this integral and only integrate from 01 Also, we can pull out the pie and foil so we get to times pi tongues integral from 0 to 1 of one minus two x squared plus X to the fourth DX and then taking anti derivatives. We get two pi times X minus two thirds execute plus 1/5 x to the fifth from 01 and then substituting. We get two pi times one minus two thirds plus 1/5 and simplifying. This is two pi times 8/15 mawr 16 15th Hi

Were given a set of curves and a line. We were asked to find the volume of the solid obtained by rotating the region bounded by these curves about this line. Then we're asked sketch the region of solid in a typical disk or washer from the solid. So the curbs that were given or why equals tu minus one half x. Why equals zero X equals one index equals two. We were asked to rotate the region about the X axis, which is the line y equals zero. So first might actually be easier to graph solid before we take the integral. So we have our region, the X Y plane. Yeah, that's equals one. X equals two. We also have Y equals zero and y equals two minus one half x. So we have we plug in, X equals one we get to minus one half is three halves point somewhere around here. And then if plugging to we get tu minus one, which is ones who point about here. And so this is our region in red and will transform this into the solid, my rotating about the X axis. So do this over here. So all we're really doing is sort of making Cone that's symmetric about the X axis. It's not a great picture here, but this is what it's supposed to be like. So this is like a part of a cone. It's had its top chopped off, and if we were to look at a cross section of this solid, it's going to be a disk like this. And so this red shape here, this is the cross section. Now to find the volume, notice that the cross section is a disk with radius to minus one half X. Therefore the area or the volume? I mean, we found using the area. The area of the disc is high times two, minus one half X squared. So the volume is going to be the integral from 1 to 2 of a of X DX area, which is the same as integral from 1 to 2 of pi times two minus one half X squared. The X miss simplifies two pi times three integral from one to of four, minus two x plus 1/4 X squared DX and taking anti derivatives. We get high times four x minus X squared plus 1/12 execute Evaluated from 1 to 2. This is PI. Times eight minus four plus 8/12 minus four minus one plus 1. 12. This simplifies two pi times one plus 7/12 which is 19 12th Hi.


Similar Solved Questions

5 answers
(hrann;In pcanaiac Gon F4ittaate esubiscitoWthe
(hrann;In pcanaiac Gon F4itt aate e subiscito Wthe...
5 answers
Question 1 (27 pts )health economist uses data enrollment in health insurance plan Di and doctor visits Y to estimate the population regression function (PRF) Y B1 + BzDi U by using the following sample:(Gnupa)ocIAr"Acotmaat9.1+01D; The benchmark group is not enrolled in a health insurance plan.
Question 1 (27 pts ) health economist uses data enrollment in health insurance plan Di and doctor visits Y to estimate the population regression function (PRF) Y B1 + BzDi U by using the following sample: (Gnupa) ocIAr "Acotmaat 9.1+01D; The benchmark group is not enrolled in a health insurance...
5 answers
Find the radius of convergenceof the series46nFind the interval, I, of convergence of the series. (Enter your answer using interval notation:Need Help?Read ItTalk toa Tutor
Find the radius of convergence of the series 46n Find the interval, I, of convergence of the series. (Enter your answer using interval notation: Need Help? Read It Talk toa Tutor...
5 answers
2w AND find all solutions8 find solutions 0 < x'3 tanx= U0
2w AND find all solutions 8 find solutions 0 < x '3 tanx= U 0...
5 answers
What volume of a 2.00 M aqueous KOH solution would be needed to neutralize 150.0 mL of 0.0450 M aqueous HCI?1ptsSubmit AnswerIncorrect. Tries 1/5 Previous TriesWhat volume of a 2.00 M aqueous KOH solution would be needed to neutralize 20.00 mL of 5.00 M aqueous HzSO4?1pts
What volume of a 2.00 M aqueous KOH solution would be needed to neutralize 150.0 mL of 0.0450 M aqueous HCI? 1pts Submit Answer Incorrect. Tries 1/5 Previous Tries What volume of a 2.00 M aqueous KOH solution would be needed to neutralize 20.00 mL of 5.00 M aqueous HzSO4? 1pts...
5 answers
Decision Build Build Buy Buy Contract ContractAdjustment Simple_ Difficule Minor changes Major Changes Minor Changes Major Changes_ProbabilityExpected Cost_ 300.000.000 IDR 600 OOQ OOQ IDR 250.000.000 IDR 500.O00.000 IDR 225.000.000 IDR 450.000.000 IDR
Decision Build Build Buy Buy Contract Contract Adjustment Simple_ Difficule Minor changes Major Changes Minor Changes Major Changes_ Probability Expected Cost_ 300.000.000 IDR 600 OOQ OOQ IDR 250.000.000 IDR 500.O00.000 IDR 225.000.000 IDR 450.000.000 IDR...
5 answers
How can any given number be represented as the sum of two parts so that their product is a maximum?
How can any given number be represented as the sum of two parts so that their product is a maximum?...
5 answers
Formulate a plausible mechanism for the hydration of ethyne in the presence of mercuric chloride. (Hint: Review the hydration of alkenes catalyzed by mercuric ion, Section $12-7 .)$
Formulate a plausible mechanism for the hydration of ethyne in the presence of mercuric chloride. (Hint: Review the hydration of alkenes catalyzed by mercuric ion, Section $12-7 .)$...
5 answers
Graph each polynomial function by following Steps 1 through 5 on page 347. $f(x)=x(1-x)(2-x)$
Graph each polynomial function by following Steps 1 through 5 on page 347. $f(x)=x(1-x)(2-x)$...
5 answers
Sample of slze n = 78 drawn from normal population whose standard deviation isThe sample mean X-50.42.Part of 2(a) Construct 98% confidence interval for Round the answer to at least two decimal places:98% confidence Interva for the mean#<Part 2 of 2Watwould the conlidence Interi canstructcc approximately normepart (0) be valld? Explaln.(D) If the populationThe confidence interval constructed part (a) (Choose one) (Choose one) large.be valld since the camoie
sample of slze n = 78 drawn from normal population whose standard deviation is The sample mean X-50.42. Part of 2 (a) Construct 98% confidence interval for Round the answer to at least two decimal places: 98% confidence Interva for the mean #< Part 2 of 2 Wat would the conlidence Interi canstruct...
5 answers
The force in diagram 3 is in equilibrium: What are the values of 019090Go_82120diagram 30 = 44.b. 0 = 49.c. 0 = 66.
The force in diagram 3 is in equilibrium: What are the values of 0 190 90 Go_ 82 120 diagram 3 0 = 44. b. 0 = 49. c. 0 = 66....
5 answers
1 14 HNO, L solutton, elassily 23.596 these compounds CH COOH 1 Wcak 1 strong 1 Resourcos Muco Jomasuv } 1 strong Give Up? Strong base bases, [ wcak bases; 1 Attempt 4
1 14 HNO, L solutton, elassily 23.596 these compounds CH COOH 1 Wcak 1 strong 1 Resourcos Muco Jomasuv } 1 strong Give Up? Strong base bases, [ wcak bases; 1 Attempt 4...
5 answers
0 ScatterplotsScatterplot 1Scatterplot 2Jdt0,.2 0.4 0.6 0.80.2 0.40.6 0.8Scatterplot 4Scatterplot 5chnnan Ase AnnAelcnnnan comapItsDonePrint
0 Scatterplots Scatterplot 1 Scatterplot 2 Jdt 0,.2 0.4 0.6 0.8 0.2 0.40.6 0.8 Scatterplot 4 Scatterplot 5 chnnan Ase Ann Aelcnnnan comap Its Done Print...
5 answers
Find the derivative of the function.q = 4xs +7x=
Find the derivative of the function. q = 4xs +7x =...
5 answers
What size is the augmented cocflicieni matrix for # system of 3 equations in vunables?In general, is matrix addition commutalive"
What size is the augmented cocflicieni matrix for # system of 3 equations in vunables? In general, is matrix addition commutalive"...
5 answers
Metal block suspended from spring scale in air causes the scale to read value of 5.35 When the suspended block submerged in water the spring scale now reads 3.78 Calculate the density (in kqm ) of the block: dlagram In requlred part 01 your JOlutlen:Scale3 4le3ko/m?
metal block suspended from spring scale in air causes the scale to read value of 5.35 When the suspended block submerged in water the spring scale now reads 3.78 Calculate the density (in kqm ) of the block: dlagram In requlred part 01 your JOlutlen: Scale 3 4le3 ko/m?...

-- 0.020038--