4

Integrate f(x,y) = X+y over the curve C: x2+y2=49 in the first quadrant from (7,0) to (0,7).fc (x+y) ds(Simplify your answer:)...

Question

Integrate f(x,y) = X+y over the curve C: x2+y2=49 in the first quadrant from (7,0) to (0,7).fc (x+y) ds(Simplify your answer:)

Integrate f(x,y) = X+y over the curve C: x2+y2=49 in the first quadrant from (7,0) to (0,7). fc (x+y) ds (Simplify your answer:)



Answers

Antidifferentiate using the table of integrals. You may need to transform the integrand first. $\int \cos 2 y \cos 7 y d y$

So that's the collision bleeding from I don't know. In the sight of Simon's first me Mommy needs it was signing white sticks, homes. Sign one. You're not signing away. Yes, Myers. Okay, well, always expand this wall. Oh, these are ones minus one. And we are valuable. I knew. So we can know. First term lease. Whoa! Oh, you know, No, I won't. And the second one's you know, my small, these ones. No Waas. Oh, this is just a few Started what?

Hello. My name is Butler. And in this video I'll show how to find the partial integral of this function here. So we have integral with the boundaries from zero to pi over two and we have X saying why do I? So you have Dy meaning it is with respect to Y. And these equations questions mentions that partial integral. And again we have the white meaning. We tease with respect to Y. So this means that everything which is not a Y. Inside Inside here, we're going to treat it as a constant, meaning our X. Is a constant. So answering the question, how do we treat Constance? We know that we can just figure out a constant outside of the integral sign. So that's what I'm gonna do here. So I'm gonna put X outside the integral. So we still go integral sign from zero to pay over two and was left inside. It's fine why? And it is with respect to Y and so on the way. So progressing further, we see of our X here and was the integral of sine wine. You know that the integral saying why? It's minus course. Why? So I'll write minus close please. All right, man has caused by inside here And here. We have our boundaries from zero to pay over two pi over two. Now progressing further. Now, what we need to do is to put in the boundaries here with three of our X as our constant. And then here we have minus course Y. So if we plug in here we're gonna have minus of course pi over two. And remember we say minus, but then since it is a minus because it's going to become a positive, so we have positive cause zero here could do okay, great. And simply find this here was to have our eggs is all constant and we know that what's caused by over to cause pain over to it's true. So we're going to have zero yet. And what's Cossio? You know that cozy? Oh, it's one. And lastly, we're just left with X. So this is the partial integral of the function we have yet. Thank you for your time.

Okay, folks. So we're gonna be doing problem number 29 here. Um, so for this problem we have, we have a circle, and we're gonna be integrating a function f along, um, along the circle in the first quadrant from 20 to 0 to so before before we get started doing the integral Let's let's just get a few preliminary steps out of the way. So for a circle, you have this equation. Obviously, you have expert plus y squared equals four. And from this, you can solve for why, and that is going to be route route four, minus x squared. Um, what, you know, because we're integrating along the first quadrant. So why is always gonna be positive and why prime, which is which is a derivative with respect of the variable X, is going to be negative x over root for a minus, X squared. So that's why prime, and from this you can get DS and DS is gonna be a positive number, because that's because DS is a is the length of, like, a really, really small triangle which can be written as the X squared plus y squared. So this little length here is what we call it the s. Excuse me. My in writing is really horrible. The S. So this is the X, and this is D Y. So the S is always going to be a positive number because it's a It's the length of failure of the of this side. I forgot what this side is called. Uh, eso es is always going to posit number because it's the length, okay, and you cannot have a negative. So now that we're clear on the fact that the U. S is gonna be a positive number, we're going to Ah, plugging in the, um we're gonna do is we're gonna divide out the ex inside the square root and multiply it by back in on the outside. Okay, so we have one plus d y over the X squared, but do you buy over? DX is really just white prime. So we have white prime squared. So we have, um, X squared over four minus x squared, and this could be simplified into two over square root of four. Mine is X squared DX. Okay, So this is our DS, except, um, except when we're actually integrating the function along the curve. When we're integrating the function along this curve, the D X they were considering is actually negative. Okay, Because because this is the direction they were integrating over. And we're going when you're going over the curve in this direction, your DX, as you realize it's in, isn't this direction okay? The excess negative. But you don't want that to happen, because when you have a negative DX, your D s is Your DS is going to be negative as well, because this number right here, this factor is always gonna be positive. And when you have a negative DX, that means the SS negative. And you don't want that to happen because the SS and cannot be negative. So the way we're going to do this is we're going toe. Just insert for this problem, insert a factor of negative one just so that we don't end up with a negative DS, which is unfit sickle. Okay, so now we have all of our preliminary steps. We can just plug in everything. Um, we have f if x Why ds and from 2 to 0 x plus Route four minus X squared. That's for what that's for a That's for the function f um multiplied by D S s o. D s is going to be too over route four minus X squared, multiplied by negative DX. And now I'm gonna split this into two parts. We have zero the to two x the X over square root plus twice, 0 to 2 the X And for the first, integral. If you do ah, you substitution, Which is, um, which is a technique where you define a new variable as U equals four minus X squared. And when you define when you define this new variable, you can get D u is negative two x x and you see here you have two x t x so that you can plug it. You can plant that. You can substitute that with negative, do you and you crank out the algebra. You're going to end up with four for the first integral plus two times two because I think this is pretty obvious. So we have four plus four, which is eight. And that's the answer for this problem. We have eight. Um, thank you very much for watching, and I will see you next time


Similar Solved Questions

5 answers
39. In the molecular orbital description of CO_ A) six molecular orbitals contain electrons: B) there are two unpaired electrons: the bond order is 3_ 8 the highest-energy electrons occupy antibonding orbitals. All of the above are false.40_ Which of the following statements about the molecule 0z Is false? Its bond order is 2_ 3 The total number of electrons is 12, It is paramagnetic. It has two pi bonds_ It has one sigma bond.
39. In the molecular orbital description of CO_ A) six molecular orbitals contain electrons: B) there are two unpaired electrons: the bond order is 3_ 8 the highest-energy electrons occupy antibonding orbitals. All of the above are false. 40_ Which of the following statements about the molecule 0z I...
5 answers
[-/1 Points]DETAILSSCALCET8 6,2.025_My NoTEsASK YOUR TEACHERPRACTICE ANOTHERRefer to the figure and find the volume generated by rotating the given region about the specified line_ about ABR(L,2)Y=2n1A(LO)Need Help?HelhilJeltfainna
[-/1 Points] DETAILS SCALCET8 6,2.025_ My NoTEs ASK YOUR TEACHER PRACTICE ANOTHER Refer to the figure and find the volume generated by rotating the given region about the specified line_ about AB R(L,2) Y=2n1 A(LO) Need Help? Helhil Jeltfainna...
5 answers
Use sumor_difference formula to find the exact value of the following_21 tan 15 tan 30 21 1- tan 15 tan 308
Use sumor_difference formula to find the exact value of the following_ 21 tan 15 tan 30 21 1- tan 15 tan 30 8...
5 answers
3* MA +28|8
3* MA +2 8| 8...
4 answers
Two pair?
Two pair?...
1 answers
Identify correct dipole moment order in the following compounds (a) $\mathrm{i}>\mathrm{ii}>\mathrm{iii}$ (b) $\mathrm{ii}>\mathrm{iii}>\mathrm{i}$ (c) $\mathrm{i}>\mathrm{iii}>\mathrm{i} \mathrm{j}$ (d) $\mathrm{iii}>\mathrm{i}>\mathrm{ii}$
Identify correct dipole moment order in the following compounds (a) $\mathrm{i}>\mathrm{ii}>\mathrm{iii}$ (b) $\mathrm{ii}>\mathrm{iii}>\mathrm{i}$ (c) $\mathrm{i}>\mathrm{iii}>\mathrm{i} \mathrm{j}$ (d) $\mathrm{iii}>\mathrm{i}>\mathrm{ii}$...
5 answers
Identify the following conic sections by writing the equations in standard form and sketch graph of each equation:1. 22+y2 _ 61 + 4y+9 = 0 2. z2 + 4y2 _ 61 + l6y + 21 = 0 3. 1 _ 22 + 4y = 0 16y? + 128r + Sy _ 7 = 0 1612 + 16y2 l61 + 249 - 3 = 0
Identify the following conic sections by writing the equations in standard form and sketch graph of each equation: 1. 22+y2 _ 61 + 4y+9 = 0 2. z2 + 4y2 _ 61 + l6y + 21 = 0 3. 1 _ 22 + 4y = 0 16y? + 128r + Sy _ 7 = 0 1612 + 16y2 l61 + 249 - 3 = 0...
5 answers
Sketch the slope field for $d y / d x=x / y$ at the points marked in Figure 11.14(FIGURE CANNOT COPY)
Sketch the slope field for $d y / d x=x / y$ at the points marked in Figure 11.14 (FIGURE CANNOT COPY)...
5 answers
Liblc. 1 M Aroulctu Ibullct 1 bullet of {ass 82 E block, Thc bullet 1 1 [ 2 [ 1 Anct
Liblc. 1 M Aroulctu Ibullct 1 bullet of {ass 82 E block, Thc bullet 1 1 [ 2 [ 1 Anct...
5 answers
The average NBA ticket price for the 2018-19 season is up 14.01%from the average ticket price of $78 during the 2015-16season. What is the average ticket price in 2018-2019? Round to the nearest penny.
The average NBA ticket price for the 2018-19 season is up 14.01% from the average ticket price of $78 during the 2015-16 season. What is the average ticket price in 2018-2019? Round to the nearest penny....
5 answers
A toy train car, A, with a mass of 0.515 kg moves with avelocity of 1.10 m/s. It collides with and sticks to another traincar, B, which has a mass of 0.450 kg. Train car B is at rest.Assuming that momentum is conserved, how fast do the two train carsmove immediately after the collision? Show your work.
A toy train car, A, with a mass of 0.515 kg moves with a velocity of 1.10 m/s. It collides with and sticks to another train car, B, which has a mass of 0.450 kg. Train car B is at rest. Assuming that momentum is conserved, how fast do the two train cars move immediately after the collision? Show you...
5 answers
A parallel plate capacitor; with area 0.04 m? and distance mM) between its plates_ filled partially with dielectric of dielectric constant K-12 as shown in Fig: Q The capacitance of this capacitor (in #F) is:A21.1511,3282.450.9740.797
A parallel plate capacitor; with area 0.04 m? and distance mM) between its plates_ filled partially with dielectric of dielectric constant K-12 as shown in Fig: Q The capacitance of this capacitor (in #F) is: A2 1.151 1,328 2.45 0.974 0.797...
5 answers
When the current in a toroidal solenoid is changing at a rateof 0.0230 A/sA/s, the magnitude of the induced emfis 12.5 mVmV. When the currentequals 1.50 AA, the average flux through each turnof the solenoid is 0.00274 WbWb.How many turns does the solenoid have?
When the current in a toroidal solenoid is changing at a rate of 0.0230 A/sA/s, the magnitude of the induced emf is 12.5 mVmV. When the current equals 1.50 AA, the average flux through each turn of the solenoid is 0.00274 WbWb. How many turns does the solenoid have?...
5 answers
3v The " probability density for the random variable Xis given by f(x) = {6(Ver ~x) 0 <x<1 zero,otherwiseFind the probability density function for the new variable Y = V
3v The " probability density for the random variable Xis given by f(x) = {6(Ver ~x) 0 <x<1 zero,otherwise Find the probability density function for the new variable Y = V...
5 answers
Use separationvarablesfindDossiple product solutions for the given partial differential equation; (Use the separation constantdossil6 enter IMPOSSIBLE: )k >2kt C3 + Ceu(x, t)~07 <u(x, t) = C1e# +Cze Cze~R_R+a21 = a2 > 0,k2 _ a2a2 _u(x; t}1 = a2 > 0,k2 _ a2a2 < 0 u(x, t)1 = a2 > 0,k2 _ a2a2 > 0 u(x, t) =Need Help?Raad ItTalk to a TutorR+Z '+C4e
Use separation varables find Dossiple product solutions for the given partial differential equation; (Use the separation constant dossil6 enter IMPOSSIBLE: ) k > 2kt C3 + Ce u(x, t) ~07 < u(x, t) = C1e # +Cze Cze ~R_ R+a2 1 = a2 > 0,k2 _ a2a2 _ u(x; t} 1 = a2 > 0,k2 _ a2a2 < 0 u(x, t)...
1 answers
Write an equation for the degree-four polynomial graphed below
Write an equation for the degree-four polynomial graphed below...
5 answers
Points) Use induction to prove that for all integers 23 n" < 3"_
Points) Use induction to prove that for all integers 23 n" < 3"_...

-- 0.022599--