5

Find the area of the shaded region. 3)y = cOs2 x1y =-COS X...

Question

Find the area of the shaded region. 3)y = cOs2 x1y =-COS X

Find the area of the shaded region. 3) y = cOs2 x 1 y =-COS X



Answers

Find the area of the region.
$y=\frac{3 \cos x}{1+\sin ^{2} x}$

So here we have the interval from zero power for a sign. Explicit, ghostly next minus coast annex. So just sign next. That's the integral from power force. However, to of science, please co sign next my sign X Just close eye next. Yes, The first part will be negative. Co sign X I, however, 40 uh plus sine x Well, you have however, to and high before like is ice uh native skirt too over too. Plus one plus one minus. It's great. You over too is as to minus Ritu.

In discussion. We need to calculate the area uh of the region enclosed between these cubs. The cubs given are as vehicles to cosine X and X vehicles to one minus three exhaust pipe. And the third one is exit goes to privately which will be a straight line parallel to the axis. So first of all we will plot the graphs of these equations, so we plotted the graph uh for these three equations, this one is for what he calls to Cosine X with purple ca and it's uh straight line is for what he calls to one minus three over X. And this state line which is red is for Mexico stuck by battery and we all associated the region between these three cars. Now we can calculate the area by partitioning the X axis. The this region exchange from Mexico's 20 to access also by by three. So this area will be, can be calculated by integrating for the limit 02 uh by by three and uh as we can see the a pack of is here, this is cousin X. And the lower cup is the straight line which is why it calls to one minus three over PXE. So we can write it here as ffx minus the fx or dx. So we can write it as cosine X minus one minus trip over PXE will be minus one plus three over pipe, X dx. Now we can integrate this and we will get the area it calls to ah by integrating this, we will get cosign X will be integrated to Synnex, one will be integrated to X and Plus three over par tax will be integrated to three over pi access care by two. That will be 3/2 pi. Not access square For the limit 0 to private tree. Now by executing this limit we will get the area s uh area they will be called to when we will substitute their parliament. This will become science private resigned private tree is Route three x 2 minus X. Will be privately only and Plus three of them to buy excess care. This will become plus 3/2 Pi. Multiplied by pi. Betrayal sky will be pie scare overnight. So this area they will be called Here. Route 3/2. This will be -9 bigotry and this will become a plus. Sorry here we forgot to calculate for the that for the lower limit it will be zero so we ignored that here and here. This will become um three By over 18. That will be plus by over six. Now, by simplifying this, we will get the area is Route two x 2- by by six. So this is the area of the shaded region which is the region between the given cubs This isn't a square units square units. I hope all of you got discussion. Thank you

Hello. So here the area of the region between what we have Y. Is equal to three to the coastline of back center backs. We have wild 0 to 0 X. Is equal to zero and execute a pie. That's gonna be the the area here is the integral from zero to pi of three to the coastline of X. Times sine of back to the X. So to do this integral we're going to use a U. Substitution and let um you be equal to just co sign of acts. We have co sign of X be equal to you. And then we get that negative sine of X. The X. Is equal to D. You. So we get that when X. Is equal to zero U. Is equal to one and when X is equal to pi U. Is equal to negative one. So therefore we then get here while we get negative the integral going from one negative one of just three to the U. D. You. Okay so we're valuing this integral. This is going to give us um Well we could flip the basically instead of having negative integral this could be positively integrated. Instead of going from 12 negative one. Now we're going from negative 1 to 1 of three to the U. Do you. Okay so we evaluate that integral and we get just three to the U. Over the natural log um of three. Um And then we evaluate that from 12 negative one. So so evaluated from one Over negative 1-1. So that's going to give us three over the natural log of 3-1 over three times the national of three, which is going to give us eight Over three times the natural log of three.

Okay, let's try to sketch the region close by those two curves. And since the domains by a specified only, I need to call the curve inside That dont make so our export. Here's our x y plain. No, this is good. Okay, look said this It's over. X y plain or ex goes from negative power three to power through it. Okay. And so of X equals power three. Tension to X equals two squared three No, the ex ecos inactive power three tens Next because through back to square root. Right, Except with zero A zero and lee no tension axis at our function. So it looks like this. And for on the other hand, for the second her are two science, you know, sex look like this so we don't We need to find the end points so and points is over X equals to power three. We know science is screwed three over to have a book Piper too. So it will be square through it assed we can see it was to curves Army intersect Had those toe end point who saw a region because Tucson accidents also our function so it will play it right here here is already close the region. And as we mentioned, everything here is symmetric by this region. So we know those two parts has I have exactly same area. So we only need to calculate one off them. The more diaper too. So say I want to calculate this area. They will be integral with respect to X. Since those two curves can be represented by X and the up the boundary here is goes from zero to three power suite and things have been integral. Will be upper curve minus the lurker, which is to sort of fix Linus tension Tex okay. And instituted off this So just mine is to co sacks minus the art. Andi, do it for ten years. We know that anti do it. If attendant attention access Cave lock actually cause annex. So this hoop clause log Who's Alex? They value it at power of three two zero so well, actually cause power three. This is over half. There's just two times previous form plus log minus X equals material is it's two times conectiv to here because cause and zero is one And we know Logue y zero so minus two plus zero. This will return Here is a plus for minus two is two and a plus two times log over too. Bye. And no for this log, we can bring one bag to sign to make this love too. What I'm saying? Here we have this for a general log. It's like negative bog A over B. Did he close to lock Good or anything? All right. It's like that. You re bringing in the negative side. Take the reciprocal inside. So this were also he close to two minus two. Block two. Yeah, We're both too can be our answer.


Similar Solved Questions

5 answers
Fill in the blanks with the required reagents.
Fill in the blanks with the required reagents....
5 answers
Solve (41 In(ax logarithmic equation X) uI
Solve (41 In(ax logarithmic equation X) uI...
5 answers
47. The region inside the curve 'cos 0 and inside the circle 1/V2 in the first quadrant
47. The region inside the curve 'cos 0 and inside the circle 1/V2 in the first quadrant...
5 answers
Poiats of Infection: Zrs9x 2 t/2 fb)=
Poiats of Infection: Zrs9x 2 t/2 fb)=...
5 answers
Point) Consider the following differential equation: 2ye?xy +x+bxeexyy = 0.Find the value of b for which the equation is exact.(b) Solve the differentlal equation using the value of b found above. Use C (capital C) for any arbitrary constant:Y(x)
point) Consider the following differential equation: 2ye?xy +x+bxeexyy = 0. Find the value of b for which the equation is exact. (b) Solve the differentlal equation using the value of b found above. Use C (capital C) for any arbitrary constant: Y(x)...
5 answers
Differentiate the function using one or more of the differentiation rules. y=(4x+5)8
Differentiate the function using one or more of the differentiation rules. y=(4x+5)8...
5 answers
A soccer player kicks ball with speed of 24.0!/s atan angle of 18.09 above the horizontal_ She sees the ball hit the on the side of a hill 25.0 meters away. Draw diagram of the situation indicating distances and the path Of the ball.Determine the time of flightb. Determine the height of the ball as it lands on the hill.d. Determine the final velocity and angle of impact (put the angle on your diagram).
A soccer player kicks ball with speed of 24.0!/s atan angle of 18.09 above the horizontal_ She sees the ball hit the on the side of a hill 25.0 meters away. Draw diagram of the situation indicating distances and the path Of the ball. Determine the time of flight b. Determine the height of the ball a...
5 answers
Given the set WcR', W={ (a,b, C,d) €R4| a-2b+c-4d=0}. Determine whether W is subspace of the vector space R4 or not: ii) Find basis for W and find dim(W). iii) Construct basis for R4 containing the basis that is obtained in part (ii) .Note: Write all your calculations and steps ofyour solution in details to the below empty field_
Given the set WcR', W={ (a,b, C,d) €R4| a-2b+c-4d=0}. Determine whether W is subspace of the vector space R4 or not: ii) Find basis for W and find dim(W). iii) Construct basis for R4 containing the basis that is obtained in part (ii) . Note: Write all your calculations and steps ofyour so...
5 answers
P. Porter,"Westernizing' Women's Risks? Breast Cancer in Lower-Income Countries," New England Journal of Medicine 358 (2008): 213-216.
P. Porter,"Westernizing' Women's Risks? Breast Cancer in Lower-Income Countries," New England Journal of Medicine 358 (2008): 213-216....
5 answers
Jons:7So_ 700It IA ViuEuesuuUe8leZoi6t:9n s4R891 Ueti1o o WaTedr20172 Jolte933 eunbe48; 791 4817 0 4891+0 Eoamas13n3n Wbe AniUeTZ0177X319 2, 8el7o9019 Jonsed1448514 Jaenan20182: Jonse87AJ0jue loueue40361 488LTL J8n14 496449 4051 989 EabedM148114 WmOnBred6J0187}864 ESz0 30 Bel 8814 3lia701ees olor3 ee20192: Jonel70521S Jose:Kona WLoiee2019TX10300 Joneut4J01602 Eaee149385 JeStS70102:80018JWBWS41409,11749)
Jons: 7So_ 700It IA Viu Euesuu Ue8le Zoi6t: 9n s 4R891 Ueti 1o o WaTedr 20172 Jolte 933 eunbe 48; 791 4817 0 4891+0 Eoamas 13n3n Wbe Ani UeT Z0177X 319 2, 8el7o 9019 Jonsed 1448514 Jaenan 20182: Jonse 87A J0jue loueue 40361 488LTL J8n14 496449 4051 989 EabedM 148114 WmOn Bred6 J0187} 864 ESz0 30 Be...
5 answers
Use the Newton'$ method to find the all solutions to the following equations:1=1+2Hint: One of the solution is in the range -1.5 < x < -0.5 and the other solution is in the range 0.5 < x < 1.5_
Use the Newton'$ method to find the all solutions to the following equations: 1=1+2 Hint: One of the solution is in the range -1.5 < x < -0.5 and the other solution is in the range 0.5 < x < 1.5_...
5 answers
Match each of the proteins needed for human health to the type of transgenic organism that produces it:PlantsGoatsBacteriaMatch each of the options bove to the items below:InsulinVaccine proteinsAntithrombin III
Match each of the proteins needed for human health to the type of transgenic organism that produces it: Plants Goats Bacteria Match each of the options bove to the items below: Insulin Vaccine proteins Antithrombin III...
5 answers
Activity #1: Escherichia coliE. coli culture with OD600 of 1 has about 8x108 CFU/mLCalculating the cell density of the originalovernight culture (tube A). OD600 of “B” is 0.018. Total dilution of B 1:10^21mL of culture A diluted into 99 mL of sterile H2O
Activity #1: Escherichia coli E. coli culture with OD600 of 1 has about 8x108 CFU/mL Calculating the cell density of the original overnight culture (tube A). OD600 of “B” is 0.018. Total dilution of B 1:10^2 1mL of culture A diluted into 99 mL of sterile H2O...
5 answers
Using Taylor series colnt Find the Taylor series for f (x) cs centered at a T You can simply write out the first 3 4 terms of the series Use your Tavlor series from part (a) to approximate Cos(170" Wvith error less than 0.0001. polnn Be sure to state how many terms you had to add:
Using Taylor series colnt Find the Taylor series for f (x) cs centered at a T You can simply write out the first 3 4 terms of the series Use your Tavlor series from part (a) to approximate Cos(170" Wvith error less than 0.0001. polnn Be sure to state how many terms you had to add:...
5 answers
Ch 8-12: What is the product of the reaction sequence shown?2Kor Nzo4
Ch 8-12: What is the product of the reaction sequence shown? 2Kor Nzo4...

-- 0.019151--