5

Use Green's Theorem to evaluate the line integral fc ry dr + COS ydy where C is the triangle with vertices at (0,0), (2,0), and (2,4}. Draw the curve and shade...

Question

Use Green's Theorem to evaluate the line integral fc ry dr + COS ydy where C is the triangle with vertices at (0,0), (2,0), and (2,4}. Draw the curve and shade the region D (assume the curve is traced out one time in the counterclockwise direction):

Use Green's Theorem to evaluate the line integral fc ry dr + COS ydy where C is the triangle with vertices at (0,0), (2,0), and (2,4}. Draw the curve and shade the region D (assume the curve is traced out one time in the counterclockwise direction):



Answers

Use Green’s theorem to evaluate line integral $\int_{C} \sin \left(x^{3}\right) d x+2 y e^{x^{2}} d y, $ where $C$ is a triangular closed curve that connects the points $(0,0),(2,2),$ and $(0,2)$ counterclockwise.

Okay. Today I'm going to show you how to use the greens hearing. So first thing we write down the lyinto go here, his lie integral. And I think it's counter cork rice here, here and here. So when you're doing the green Syrian, I think it's the county court. Right? So orientation, it's all rented. Contact Crock. Right? So for this one, here is Q And here is P. You write down something like that. So? So if you cannot remember this thing, you can write like this. 60 N d x d d. Why here? I think here is Q and he s P So here, piece for the X right. And the Q is for the Why so for this one is I. And this one is J here. We can write down like this for the line integral. Then we have we need to figure out the up, around and lower bound here for this one is why equal to X. Otherwise why would you two x and X from 0 to 2? So here and you think everybody knew how to take this into girls. So the result is 12

Have problem. One of the threes and green salmon value at the following Integral. Sympathize to two. I'm on a zero d a pregnant or limits simplifying this comes out of three.

We have? Yes. Six. Why equals zero and G weeks. Envoy equals ex wife using getting interior. We have integer over the closed with C. If new Roy minus she takes equals Digger, You get in off the bunch of the with you. If with respect to X plus, Bush did it with you. Was she respect? Boy, do that equals two in particular. What? More foi me? It is a right triangle. Who's right? Our ability to the exceeds. So that equals two the double integral from zero to to and from zoo 24 minus two x off X Do I ds the sequence to integer from zero to to well minus two. Excess quipped just for kicks. Bigs, That equals toe. Yeah, work the thank you.

Okay, so in this video, we're acid. It's really people lining to grow But the falling so x x times y squared the x plus two x squared y que y and the way where Which we're gonna determine the slide into broke iss queens Now, were you during the mind to go along the path? See that we have that sees to find That's the falling triangle. So we go from 00 to to from 2 to 2 to four, then from 24 back issues. Here's the thing. The first thing we notice is this line right here from 00 to 2. This we can write it as wise. Why won't you plug in Europe or acts They're going to get 00 you for Morgan. Still for excellent again, why is equal to two? So this is just the straight lines of the line from zero. Resorted to two is just straight by. Would you call what you just equal to wise equal to fix. But then to go from 00 to 4 again, this is just a straight line And then we know that the smoke off the slopes of the Y intercept in syrup. But the slope of this line is just y tu minus. Why one divided by X to buying sex work. It's just four minus zero, divided by two minus zero, which is just to all right, so this is a great thing. So here we know that this line right over here just why is equal to X The spine right over here is why people did to us this simple in your All right. So now this is our formula. For that was it screens here. So now we need to take the derivative two x squared bar with respect, effects and derivative of exports were respectable Oy. So we get it's more x y minus two x one, which is just talks. But here is a key thing going to set our limits of integration. So first of all, our why goes for what? What, as we notice, are wide starts. So please register vertical life you see that are lying started. Why is equal to X on the end that wise people to two weeks with that? Those are limits of integration with respect on our limits of integration with respect to X, we see that of X starts at zero and then goes full of related to. So our limits of integration with perspective axes just from zero to. So this is how we set our limits right here. So we go from extra two X then from zero to All right, so now again. So we got or experience to experts to Rex. Now, this is the integral. This is a double general. We have to We have to deal with. And I was saying to grow to export respect. What? Well, again to excess constant because there is no wall unit. The interval. While I respect your why is, uh, why square divided by two. So the two cancel and just left with ex voice our limits of integration off extra two X. So now we're gonna plug in x two x and X until why is either into Why? So Get this. Since you called right here. Three have X ties to X square. It just works. Cube minus x times X squared. Excuse. So what? We get this three excuse And now we have to integrate this with there. So what? We get this three extra power for divided by four on our limits if integration are from security. So when we plug in to we have free time student problem working. But for just just three times, 16 by four, it is just so 16 divided by four. Its force, or three times four is 12. Then here we have three times over the power of Ford for this entire thing is just that means that are lying trouble which we evaluated using Clean Spear. Um, is he wanted to?


Similar Solved Questions

5 answers
Question 3 (70 Points) Use Muller's Method for the below function in the interval [0 , 2] and find the value of € and a for the following quadratie equation p(v) av + bv + €f(x) =x3 +3x2 _ 1
Question 3 (70 Points) Use Muller's Method for the below function in the interval [0 , 2] and find the value of € and a for the following quadratie equation p(v) av + bv + € f(x) =x3 +3x2 _ 1...
5 answers
(6 pts) continuous random variable X has depsity (pdf)f(z) 9 22 0 < = < 3. Find the median value of X_ This is defined to be the number m satisfying the equation F(m) = P[X < m] = 0.5, where F is the cdf of X_10. (6 pts) Suppose X is a random variable whose moment generating function is 25e2t mx (t) 35et)2Find E[X]-
(6 pts) continuous random variable X has depsity (pdf) f(z) 9 22 0 < = < 3. Find the median value of X_ This is defined to be the number m satisfying the equation F(m) = P[X < m] = 0.5, where F is the cdf of X_ 10. (6 pts) Suppose X is a random variable whose moment generating function is 2...
5 answers
DEmawaxa E Wo JW 1 1 BW 3 E ba 2 01 2 6azi E 3 animallhider E 1 Dne n E 1 Elem J PHB Naa KM W1
D Emawaxa E Wo JW 1 1 BW 3 E ba 2 01 2 6azi E 3 animallhider E 1 Dne n E 1 Elem J PHB Naa KM W 1...
5 answers
Tutorial ExorciseFind the derivative of the logarithmic function. ((x) = In(x57
Tutorial Exorcise Find the derivative of the logarithmic function. ((x) = In(x57...
5 answers
89.56 MHz0.04 ml : 0.5 ml CDCLHe = 1.5 +Imi Hd?nHb 1 Ha = 110
89.56 MHz 0.04 ml : 0.5 ml CDCL He = 1.5 + Imi Hd?n Hb 1 Ha = 1 10...
5 answers
Problen OnOLct Ghethe group o polvnonials withreal eoeflicieuts Aler adkition of polynomials_ Deline the' mAp <of(m))fO)s with integratiu cOnstunt st t0 be zero:(a) Does & defite group hommorphist" Explain vour ALSWET :(b) Is 0 iujective? Explain your hSHrDoes dcfine BTOup isomorphisu? Explain YOur AnSWOT .
Problen OnO Lct Ghethe group o polvnonials withreal eoeflicieuts Aler adkition of polynomials_ Deline the' mAp < of(m)) fO)s with integratiu cOnstunt st t0 be zero: (a) Does & defite group hommorphist" Explain vour ALSWET : (b) Is 0 iujective? Explain your hSHr Does dcfine BTOup iso...
5 answers
0-/4 Points]DETAILSSCALC8 14.6.041.MY NOTESASK YOUR TEACHERPRACTICE ANOTHERFind equations the folloning- (z - 912 (a) the tangent plane(2,3, 11)(b} the normal line (xlt) st) z(t))Need Help?
0-/4 Points] DETAILS SCALC8 14.6.041. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find equations the folloning- (z - 912 (a) the tangent plane (2,3, 11) (b} the normal line (xlt) st) z(t)) Need Help?...
5 answers
Moment of inertia about a line A wedge like the one in Exercise 22 has $a=4, b=6,$ and $c=3 .$ Make a quick sketch to check for yourself that the square of the distance from a typical point $(x, y, z)$ of the wedge to the line $L: z=0, y=6$ is $r^{2}=(y-6)^{2}+z^{2}$ Then calculate the moment of inertia of the wedge about $L$
Moment of inertia about a line A wedge like the one in Exercise 22 has $a=4, b=6,$ and $c=3 .$ Make a quick sketch to check for yourself that the square of the distance from a typical point $(x, y, z)$ of the wedge to the line $L: z=0, y=6$ is $r^{2}=(y-6)^{2}+z^{2}$ Then calculate the moment of ine...
1 answers
Braking Load A Toyota Sienna with a gross weight of 5300 pounds is parked on a street with an $8^{\circ}$ grade. See the figure. (Figure can't copy) Find the magnitude of the force required to keep the Sienna from rolling down the hill. What is the magnitude of the force perpendicular to the hill?
Braking Load A Toyota Sienna with a gross weight of 5300 pounds is parked on a street with an $8^{\circ}$ grade. See the figure. (Figure can't copy) Find the magnitude of the force required to keep the Sienna from rolling down the hill. What is the magnitude of the force perpendicular to the hi...
5 answers
Based on the reaction below which two chemicals form a conjugateacid base pair?CH3NH2(aq)+H2O(i)ch3NH-+(aq)+OH-(aq)A) CH3NH3+ andOH-B) H2O and OH-C) CH3NH2 and H2OD) CH3NH2 and OHE) None of these
Based on the reaction below which two chemicals form a conjugate acid base pair? CH3NH2(aq)+H2O(i)ch3NH-+(aq)+OH-(aq) A) CH3NH3+ and OH- B) H2O and OH- C) CH3NH2 and H2O D) CH3NH2 and OH E) None of these...
5 answers
C.) Complete this reaction.CH3 CH3
c.) Complete this reaction. CH3 CH3...
5 answers
ONLINE- MAT1033 - CRN10316 - Spring 2020 (1)Homework: Section 8.1 Homework Score: 0 of pt 108.1.47The sides of the box shown are labeled with the dimensions in feet: What is the value of x if the volume of the box is 24 cubic feet?Enter your answer In Ine answer box and then click Check Answe
ONLINE- MAT1033 - CRN10316 - Spring 2020 (1) Homework: Section 8.1 Homework Score: 0 of pt 10 8.1.47 The sides of the box shown are labeled with the dimensions in feet: What is the value of x if the volume of the box is 24 cubic feet? Enter your answer In Ine answer box and then click Check Answe...
5 answers
The compound shown below used as disinfectant: Propose synthesis of this compound starting {rom benzene: For full credit you need to write out allthe steps showing the reagents used for each reactionas well as the product ofeach step: For reactions that produce both ortho and para isomers_ assume that the para isomer is the major product: This is not mechanism problem please don't show electron arrowsSO,H
The compound shown below used as disinfectant: Propose synthesis of this compound starting {rom benzene: For full credit you need to write out allthe steps showing the reagents used for each reactionas well as the product ofeach step: For reactions that produce both ortho and para isomers_ assume th...
5 answers
1.Potential gradient defined bya.E= F /Qb.E=V/Mc.E=V/Fd.E=Q/t2.Choose the value of the resistance for a 100 W, 200 V lamp from the following option.a.100 Ohmsb.1600 Ohmsc.400 Ohmsd.200 Ohms3.Which element allows the electric current to flow in it?a.Paperb.Carbonc.Aird.Procelain4.Which of the following Properties change with direction of operation?a.Unilateral Circuitb.Linear Circuitc.Bilateral Circuitd.Non Linear Circuit
1.Potential gradient defined bya.E= F /Qb.E=V/Mc.E=V/Fd.E=Q/t2.Choose the value of the resistance for a 100 W, 200 V lamp from the following option.a.100 Ohmsb.1600 Ohmsc.400 Ohmsd.200 Ohms3.Which element allows the electric current to flow in it?a.Paperb.Carbonc.Aird.Procelain4.Which of the followi...
5 answers
21. Find, t0 the nearest unit the length of te longer leg of a right triangle if the length of the hypotenuse is 8, and the measure of an acute angle is 22_
21. Find, t0 the nearest unit the length of te longer leg of a right triangle if the length of the hypotenuse is 8, and the measure of an acute angle is 22_...
5 answers
(1 point) Find the distance the point P(-1, -5, 1), is to the plane through the three points Q(-3, 22, 4) , R(, 6,-7) , and S(O, 3, 0).
(1 point) Find the distance the point P(-1, -5, 1), is to the plane through the three points Q(-3, 22, 4) , R(, 6,-7) , and S(O, 3, 0)....
5 answers
EquiredThe diagrams show the position of the pointer of an ammeter and a voltmeter when performs an experiment for the verification of Ohm's law. studeng Find the relative error in resistance where V=IRNote Write answer 2 decimal point (2 Points)0.608
equired The diagrams show the position of the pointer of an ammeter and a voltmeter when performs an experiment for the verification of Ohm's law. studeng Find the relative error in resistance where V=IR Note Write answer 2 decimal point (2 Points) 0.6 08...

-- 0.019225--