Question: Use Green's Theorem to evaluate the line integral around the given closed curve. (oint_{C} y e^{x} d x+x e^{y} d y), where (C) is the

Use Green's Theorem to evaluate the line integral around the given closed curve.

THEOREM 1 Green's Theorem Let D be a domain whose boundary 3D

$\oint_{C} y e^{x} d x+x e^{y} d y$, where $C$ is the triangle with vertices $(-1,0),(0,4)$, and $(0,1)$, oriented counterclockwise

THEOREM 1 Green's Theorem Let D be a domain whose boundary 3D is a simple closed curve, oriented counterclockwise. If F and F have continuous partial deriva- tives in an open region containing D, then Fi f Fdx + Fdy = = 16 (f/ TL (SF2-F1) a dA D

Step by Step Solution

★★★★★

3.28 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To evaluate the line integral around the given closed curve using Greens Theorem we first need to identify the vector field whose line integral we are ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!

Use Green's Theorem to evaluate the line integral around the given closed curve. Where C consists of the arcs y = x2 and y = (x, 0 ( x ( 1, oriented clockwise? y? dx - x dy.

Use Green's Theorem to evaluate the line integral around the given closed curve. Where C is the rectangle 1 ¤ x ¤ 2, 2 ¤ y ¤ 3, oriented counterclockwise? xy3dx 3ydy,

Use Green's Theorem to evaluate the line integral around the given closed curve. $\oint_{C} x y^{3} d x+x^{3} y d y$, where $C$ is the boundary of the rectangle \(-1 \leq x \leq 2,-2 \leq y \leq...

Use Green s Theorem to evaluate the line integral along the given positively oriented curve Scxydx x y dy C is counterclockwise around the triangle with vertices 0 0 1 0 and 1 4

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = Vf. (If the vector field is not conservative, enter DNE. ) F (x, y) = (7x6 y + y - 4)i+ (x7 - 4xy...

Use Green's theorem to evaluate the line integral along the given positively oriented curve. cos(y) dx + x2 sin(y) dy, C is the rectangle with vertices (0, 0), (4, 0), (4, 2), (0, 2) DETAILS SCALCET9...

2. [-/1 Points] DETAILS SCALC9 16.4.005. Use Green's theorem to evaluate the line integral along the given positively oriented curve. ye* dx + 2e* dy, C is the rectangle with vertices (0, 0), (3, 0),...

Use Greens Theorem to evaluate the line integral along the given positively oriented curve. c xy 2 dx + 2x 2 y dy, C is the triangle with vertices (0, 0). (2, 2), and (2, 4) Data from Green's...

Use Green's theorem to evaluate the line integral along the given positively oriented curve. ye dx + 2e dy, C is the rectangle with vertices (0, 0), (2, 0), (2, 6), and (0, 6) JcEvaluate the surface...

1. [-/0.4 Points] DETAILS LARCALC11 15.4.005. Verify Green's Theorem by evaluating both integrals ON aM ax ay dA for the given path. C: boundary of the region lying between the graphs of y = x and y...

During 2020, Quinn Company sold equipment with a book value of $90,000 for proceeds of $109,000. The company purchased new equipment for $240,000 by signing a long- term note payable. No other...

Sisson Corporation reports operating expenses of $80,000 excluding depreciation expense of $15,000 for 2014. During the year, prepaid expenses decreased $6,600 and accrued expenses payable increased...

What is the APY for a savings account with a $ 2 5 0 balance that receives $ 9 interest for the year? Select one: a . 2 . 5 % b . 1 0 . 4 % c . 4 . 3 2 % d . 2 0 . 8 % e . 3 . 6 %

3. Does the picketing in this case fall under the proviso? Explain.

Sketch and identify a quadric surface that could have the traces shown. Traces in x = k Traces in y = k k= 1 k=0 k= 2

Sketch and identify a quadric surface that could have the traces shown. Traces in x = k Traces in z = k ZA k= 2 k= 1 -k = 0 k= 0 k= 2 k=2 k=1 k=0

Reduce the equation to one of the standard forms, classify the surface, and sketch it. y 2 = x 2 + 1/9z 2

write a respond about chapter 4 art of the ancient aegean

Java assignment Consider the selection sort algorithm we saw in lecture. Suppose A=(12,4,20,6,2,11). Execute selection sort on A and write down what the list looks like after each iteration of the...

At January 1, 2020, Swifty Inc. has beginning inventory of 4400 surfboards. Swifty estimates it will sell 16200 units during the first quarter of 2020 with a 10% increase in sales each quarter....