Question

F(x, y) = yi + xj (a) Show F is conservative Given your answer in (a)...

F(x, y) = yi + xj
(a) Show F is conservative

Given your answer in (a) show that the following integrals have the same value.
(b) The line segment y = x from (0,0) to (1,1).

(c) The parabola y=x^2 from (0,0) to (1,1).

(d) The cubic y=x^3 from (0,0) to (1,1).

(e) The b, c and d are examples of what property resulting from part a?
Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For each vector field F~ (x, y) = hP(x, y), Q(x, y)i, find a function f(x,...
For each vector field F~ (x, y) = hP(x, y), Q(x, y)i, find a function f(x, y) such that F~ (x, y) = ∇f(x, y) = h ∂f ∂x , ∂f ∂y i by integrating P and Q with respect to the appropriate variables and combining answers. Then use that potential function to directly calculate the given line integral (via the Fundamental Theorem of Line Integrals): a) F~ 1(x, y) = hx 2 , y2 i Z C F~ 1...
1. a) Let F(x,y) = hcosy,−xsiny + 2yi. Show that F is conservative, and find a...
1. a) Let F(x,y) = hcosy,−xsiny + 2yi. Show that F is conservative, and find a function φ such that ∇φ(x,y) = F(x,y). b) Use the result from part a) to find R C F · Tds, where C is given by r(t) = ht,πti,0 ≤ t ≤ 1.
(a) Is the vector field F = <e^(−x) cos y, e^(−x) sin y> conservative? (b) If...
(a) Is the vector field F = <e^(−x) cos y, e^(−x) sin y> conservative? (b) If so, find the associated potential function φ. (c) Evaluate Integral C F*dr, where C is the straight line path from (0, 0) to (2π, 2π). (d) Write the expression for the line integral as a single integral without using the fundamental theorem of calculus.
Is the function f(x,y)=x−yx+y continuous at the point (−1,−1)? If not, why is the function not...
Is the function f(x,y)=x−yx+y continuous at the point (−1,−1)? If not, why is the function not continuous? Select the correct answer below: A. Yes B. No, because lim(x,y)→(−1,1)x−yx+y=−1 and f(0,0)=0. C. No, because lim(x,y)→(−1,1)x−yx+y does not exist and f(0,0) does not exist. D. No, because lim(x,y)→(0,0)x2−y2x2+y2=1 and f(0,0)=0.
Given the force field F(x, y) = (x − y, 4x + y^2 ), find the...
Given the force field F(x, y) = (x − y, 4x + y^2 ), find the work done to move along a line segment from (0, 0) to (2,0), along a line segment from (2,0) to (0,1), and then along another line to the point (−2, 0). Show your work.
You are given that the function f(x,y)=8x2+y2+2x2y+3 has first partials fx(x,y)=16x+4xy and fy(x,y)=2y+2x2, and has second...
You are given that the function f(x,y)=8x2+y2+2x2y+3 has first partials fx(x,y)=16x+4xy and fy(x,y)=2y+2x2, and has second partials fxx(x,y)=16+4y, fxy(x,y)=4x and fyy(x,y)=2. Consider the point (0,0). Which one of the following statements is true? A. (0,0) is not a critical point of f(x,y). B. f(x,y) has a saddle point at (0,0). C. f(x,y) has a local maximum at (0,0). D. f(x,y) has a local minimum at (0,0). E. The second derivative test provides no information about the behaviour of f(x,y) at...
Let F(x,y,z) = yzi + xzj + (xy+2z)k show that vector field F is conservative by...
Let F(x,y,z) = yzi + xzj + (xy+2z)k show that vector field F is conservative by finding a function f such that and use that to evaluate where C is any path from (1,0,-2) to (4,6,3)
Consider the vector force field given by F⃗ = 〈2x + y, 3y + x〉 (a)...
Consider the vector force field given by F⃗ = 〈2x + y, 3y + x〉 (a) Let C1 be the straight line segment from (2, 0) to (−2, 0). Directly compute ∫ C1 F⃗ · d⃗r (Do not use Green’s Theorem or the Fundamental Theorem of Line Integration) (b) Is the vector field F⃗ conservative? If it is not conservative, explain why. If it is conservative, find its potential function f(x, y) Let C2 be the arc of the half-circle...
Evaluate H C F · dr, if F(x, y, z) = yi + 2xj + yzk,...
Evaluate H C F · dr, if F(x, y, z) = yi + 2xj + yzk, and C is the curve of intersection of the part of the paraboliod z = 1 − x 2 − y 2 in the first octant (x ≥ 0, y ≥ 0, z ≥ 0) with the coordinate planes x = 0, y = 0 and z = 0, oriented counterclockwise when viewed from above. The answer is pi/4+4/15
Consider F and C below. F(x, y, z) = yz i + xz j + (xy...
Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 18z) k C is the line segment from (1, 0, −3) to (4, 4, 1) (a) Find a function f such that F = ∇f. f(x, y, z) = (b) Use part (a) to evaluate C ∇f · dr along the given curve C.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT