5

21_ Findthe mnean of f : 1+ (22 + H)Vz - 3 OHL [7 , 12]; the area of the region bounded by the curve y = 6 - x 22 and the D-axis; the area of the region bounded by ...

Question

21_ Findthe mnean of f : 1+ (22 + H)Vz - 3 OHL [7 , 12]; the area of the region bounded by the curve y = 6 - x 22 and the D-axis; the area of the region bounded by the curves y = 6 - 1 - 12 and J = 23 212 31; the length of the arc of the curve y? 913 from (0,0) to (1,2/3) .

21_ Find the mnean of f : 1+ (22 + H)Vz - 3 OHL [7 , 12]; the area of the region bounded by the curve y = 6 - x 22 and the D-axis; the area of the region bounded by the curves y = 6 - 1 - 12 and J = 23 212 31; the length of the arc of the curve y? 913 from (0,0) to (1,2/3) .



Answers

$11-20=$ Sketch the region enclosed by the given curves and
find its area.

$$y=12-x^{2}, \quad y=x^{2}-6$$

The first thing to point out is that area needs to be positive. Yeah. Male. But an error that needs to be positive. So if you were to look at the graph of x squared minus one, Y equals x squared minus one. Then we want the area in here. But if you did the integral of that, you're going to get a negative answer. So what I'm gonna do is just do the absolute value of that, that answer X squared minus one dx. Um and then they also tell you that they care about from negative 1-1 the X values which happened to be on the y axis. Uh So when you do this problem, add volunteer exponents And multiply by the reciprocal of your new exponents and we're going from negative 1-1. But as I plug in one in there, So one cubed is still one. Um And then minus or negative on when cuba is negative one last one. What you'll see is I get the answer of negative two thirds minus uh two thirds which gives me an answer of negative four thirds. Remember I discussed the absolute value of all of that In your area should be positive for 30 cents. Yeah.

For this problem were given to functions. Y goes The absolute value of X shown here in blue and y equals X squared minus two shown here and cream were asked to identify the region between the curves, which I've done here in red, and to calculate the area. You can calculate the area in two ways you can do it is to separate inter girls, one going from negative to 01 from one. Going from X equals ear toe X equals two or you can do it is two times the area in one of those haves, since the area could be split into two equal hats. So the way I've done it is I did two times the integral from 0 to 2, so X equals zero X equals two of the function on top, minus the function on the bottom, which would be X since from 0 to 2, it's a pause. It's a slope with a It's a line with a slope of one so B y equals X minus the function on the bottom, which is X squared by this to so the area will be represented as two times the integral from 0 to 2 of X minus X squared, minus two DX Distributing the negative, we get two times the integral from 0 to 2 of X minus X squared plus two DX taking the integral of X. We add one to the exponents and then divide by the new exponents, so become 1/2 X squared and then x squared. We add one to the exponents divide by the new exponents, so becomes minus 1/3 x cubed. And then the constant simply gets a variable next to it. So plus two acts, we then plug in to for X. So it becomes to minus 8/3 plus four minus. And then we plug zero and fax, So just be minus zero, adding these together and then multiplying by two, you get the area to be 20/3.

For this problem were given to functions. X equals two y squared shown here in green and X equals four plus y squared. Shown here in blue, we were asked to calculate the area between the two curves shaded here in red. To do this, we're going to take the integral with respect to why from y equals negative, too. So why equals two, since those are the bounds of the shaded red region. To do this, we do the integral from negative to to to of the function on top, minus the function on the bottom when going from wyffels negative to toe y equals two four plus y squared is on top in two y squared is on bottom. Therefore, the area between the curves is the integral from negative to to to a four plus y squared, since its on top minus two Y squared says it's on the bottom. We can then combine like terms to make it the integral from negative to to to a four minus y squared D Y. The integral of a constant is simply the constant times, the variable. So before why minus the integral of y squared, you add one to the exponents and then divide by that new exponents, so becomes minus 1/3 y cube. We them insert to infer why so becomes eight minus 8/3 mightiest parentheses. And then we insert negative to infer what so parentheses. Negative eight, plus a third's adding all these numbers. Together we get 32 3rd as the area between the two curves.

For this problem were given to functions y goes for X minus X squared shown here in blue and y equals X squared. Shown here in green. The area between the two curves a shaded in red and the area between the two curves is defined by the points to 400 To find the area between the two curves will integrate with respect to X with X equals zero and X equals to being the borders of the region between the two curves and from X equals zero X equals two y equals four x minus. X squared is always the function on top, while y equals X squared is always the function on the bottom. Therefore, the area between the two curves is defined by the integral from 0 to 2 a four x minus X squared function on top nine iss X squared the function on the bottom, combining like terms. We get the integral from 0 to 2 of negative two X squared plus four x dx. To integrate this, we add one to the exponents and then divide by the new exponents. So becomes negative 2/3 x cubed. Plus we add one to the exponents and divide by the new X poem. So plus two x squared, we plug into to get negative 16 3rd plus hey minus, and then we plug in zero, which will just be minus zero. Therefore, the area between the two curves is defined as negative 16 3rd plus eight, which equals 8/3.


Similar Solved Questions

5 answers
Fon hrdroocn Jnd cnaan monanda Kethanc and Hancr (eadCH (9)+ H;Oa) 3H,(9}+CO(9)couabumdoscd rtacton vesed Arrdid Atxchat2 endothcnic_ Suppote Ittune #CH,H,O,H;end CO ts come Te redon cquilbrim stt t0 Ene nott or Kt tha muture the vesicl Ako dedde ntthe tne tablc bclonWll @uscin the compostion peturtabonschanaal ceeoaitin49-0in47perturbatio?Olet
fon hrdroocn Jnd cnaan monanda Kethanc and Hancr (ead CH (9)+ H;Oa) 3H,(9}+CO(9) couabum doscd rtacton vesed Arrdid Atxchat2 endothcnic_ Suppote Ittune #CH,H,O,H;end CO ts come Te redon cquilbrim stt t0 Ene nott or Kt tha muture the vesicl Ako dedde ntthe tne tablc bclonWll @uscin the compostion pet...
5 answers
Rolygon JeAe quadrilaeral Triag Sa Zange(qucuteraQ Tocnee TropezojdKitePana(tolcdranRcct. Rlarbu SUaA
Rolygon JeAe quadrilaeral Triag Sa Zange (qucuteraQ Tocnee Tropezojd Kite Pana(tolcdran Rcct. Rlarbu SUaA...
5 answers
Integrate the expression: $int^{3} sqrt{x}^{2} mathrm{~d} x$.
Integrate the expression: $int^{3} sqrt{x}^{2} mathrm{~d} x$....
5 answers
Let Q be the solid bounded by the paraboloid 2 3 4 V" and the Ty-plane: Applying the Divergence Theorem find the fux of the vector field F(c,8,2) = over the surlace €Q . Use the Stokes Theorem to evaluate the surfuce integral fs F(V x F) -ndS , where F(I.y, 2) 9,81sinV) and where $ ix the portion of the puraboloid above Lhe fy-plang,
Let Q be the solid bounded by the paraboloid 2 3 4 V" and the Ty-plane: Applying the Divergence Theorem find the fux of the vector field F(c,8,2) = over the surlace €Q . Use the Stokes Theorem to evaluate the surfuce integral fs F(V x F) -ndS , where F(I.y, 2) 9,81sinV) and where $ ix the...
5 answers
Find and classify the relative extrema and saddle points of the function.$$f(x, y)=e^{-x^{2}-y^{2}}$$
Find and classify the relative extrema and saddle points of the function. $$ f(x, y)=e^{-x^{2}-y^{2}} $$...
5 answers
Wfan impulse ol magnitude 800. Ns Is suppliea ol the force units ol nexrons?obleciconsiani orce "tenacts on Ihe = object for 8 time of 0.185 whatis iha magnitude
Wfan impulse ol magnitude 800. Ns Is suppliea ol the force units ol nexrons? obleci consiani orce "ten acts on Ihe = object for 8 time of 0.185 whatis iha magnitude...
5 answers
13 .- [4, points each]Determine if the series is absolutely convergent, conditionally convergent or divergent: Clearly slate the test thaL YQLLare_usingsin3n(a)(-1)" Va + 7)
13 .- [4, points each]Determine if the series is absolutely convergent, conditionally convergent or divergent: Clearly slate the test thaL YQLLare_using sin3n (a) (-1)" Va + 7)...
1 answers
Find the area of each triangle $A B C$. $C=72.2^{\circ}, b=43.8 \mathrm{ft}, a=35.1 \mathrm{ft}$
Find the area of each triangle $A B C$. $C=72.2^{\circ}, b=43.8 \mathrm{ft}, a=35.1 \mathrm{ft}$...
5 answers
Using the trigonometric substitution, the integralI =100)100is equal to the integral, in terms of 0 ,doAfter integration and substituting back to the variablethe final result is
Using the trigonometric substitution, the integral I = 100) 100 is equal to the integral, in terms of 0 , do After integration and substituting back to the variable the final result is...
5 answers
The normal time for walking in MTM-1 is 7 9 TMUlft distance_ Using this value, determine the amount of time in minutes that would be required to walk mile (5280 ft)25.03 minutes 30.03 minutes 21.45 minutes 37 54 minutes
The normal time for walking in MTM-1 is 7 9 TMUlft distance_ Using this value, determine the amount of time in minutes that would be required to walk mile (5280 ft) 25.03 minutes 30.03 minutes 21.45 minutes 37 54 minutes...
5 answers
Find three positive numbers whose sum is 27 and such that the sum of their squares is as small as possible.
Find three positive numbers whose sum is 27 and such that the sum of their squares is as small as possible....
5 answers
A furnace wall is composed of three layers, 10cm offirebrick(K1=1.560W/mk), followed by 23cm of Kaolin insulatingbrick(k2=0.073W/mK), and finally 5cm of masonry brick(k3=1.0W/mK).The temperature of the inner wall surface is 1370K and the outersurface is at 360K. What are the temperatures at the contactingsurfaces?
A furnace wall is composed of three layers, 10cm of firebrick(K1=1.560W/mk), followed by 23cm of Kaolin insulating brick(k2=0.073W/mK), and finally 5cm of masonry brick(k3=1.0W/mK). The temperature of the inner wall surface is 1370K and the outer surface is at 360K. What are the temperatures at the ...
5 answers
Pan AUsing Ihe Bohf model ol hydrogen (ind (he linear momentump= 6 62*10-25 kg * m/sPmvlous AnswersCorrectPart BUsing the Bolr nodel ol hydrogen; find the angular momentur of Ihe electron In this alomSubmllRequest AnixefProviae FeacbackMnSned
Pan A Using Ihe Bohf model ol hydrogen (ind (he linear momentum p= 6 62*10-25 kg * m/s Pmvlous Answers Correct Part B Using the Bolr nodel ol hydrogen; find the angular momentur of Ihe electron In this alom Submll Request Anixef Proviae Feacback MnSned...
5 answers
What is the chemical structure of trans- ttrans delta 12,14028 fatty acid ?
what is the chemical structure of trans- ttrans delta 12,14028 fatty acid ?...
5 answers
Find the directional derivative of the function f (€,y) = 3 22 _ 5 y2 at the point (2,4) in the direction of < 3,3 >.7 Jz 84 22 V2
Find the directional derivative of the function f (€,y) = 3 22 _ 5 y2 at the point (2,4) in the direction of < 3,3 >. 7 Jz 84 22 V2...
5 answers
Determine if b is a linear combination of 41,42,and 43. [OT 01 = AA 42 5 a3 L5]b = 11
Determine if b is a linear combination of 41,42,and 43. [OT 01 = AA 42 5 a3 L5] b = 11...
5 answers
1 1 cneer 4 are any4sung 1 inteavgeso stotateova)Find tnl acnema Fiu,bu Poims 1 1 ZILLDIFFEQMODAPTT 1 dultercntid cqudtion 804 99"9 { Soivc (ne qiven Uincntdi 1)80 equution L 11 vounios 11 IcatiansKrnsim amns sinquiur 1 1 Intncre InasuPMY NOTES
1 1 cneer 4 are any 4sung 1 inteavgeso stotateova) Find tnl acnema Fiu,bu Poims 1 1 ZILLDIFFEQMODAPTT 1 dultercntid cqudtion 8 04 99"9 { Soivc (ne qiven Uincntdi 1)80 equution L 1 1 vounios 1 1 Icatians Krnsim amns sinquiur 1 1 Intncre InasuP MY NOTES...
5 answers
1.000.9010.8010.700.600.5010.400.300.200.10
1.00 0.901 0.801 0.70 0.60 0.501 0.40 0.30 0.20 0.10...

-- 0.022579--