Question

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 of radius 2 from (2, 0) to (−2, 0) with y ≥ 0. Compute ∫ C2 F⃗ · d⃗r

Explain your work and how your answer relates to the answer to part (a).

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Sketch the vector field F⃗ (x,y)=−5i and calculate the line integral of F⃗ along the line...
Sketch the vector field F⃗ (x,y)=−5i and calculate the line integral of F⃗ along the line segment from (−5,3) to (0,4).
1. (a) Determine whether or not F is a conservative vector field. If it is, find...
1. (a) Determine whether or not F is a conservative vector field. If it is, find the potential function for F. (b) Evaluate R C1 F · dr and R C2 F · dr where C1 is the straight line path from (0, −1) to (3, 0), while C2 is the union of two straight line paths: first piece from (0, −1) to (0, 0) and then second piece from (0, 0) to (3, 0). (When applicable, use the Fundamental...
(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.
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...
Consider the vector field F = <2 x y^3 , 3 x^2 y^2+sin y>. Compute the...
Consider the vector field F = <2 x y^3 , 3 x^2 y^2+sin y>. Compute the line integral of this vector field along the quarter-circle, center at the origin, above the x axis, going from the point (1 , 0) to the point (0 , 1). HINT: Is there a potential?
. a. [2] Compute the divergence of vector field F = x 3y 2 i +...
. a. [2] Compute the divergence of vector field F = x 3y 2 i + yj − 3zx2y 2k b. [7] Use divergence theorem to compute the outward flux of the vector field F through the surface of the solid bounded by the surfaces z = x 2 + y 2 and z = 2y
Suppose F⃗ (x,y)=〈x^2+5y,7x−3y^2〉. Use Green's Theorem to calculate the circulation of F⃗ around the perimeter of...
Suppose F⃗ (x,y)=〈x^2+5y,7x−3y^2〉. Use Green's Theorem to calculate the circulation of F⃗ around the perimeter of the triangle C oriented counter-clockwise with vertices (10,0), (0,5), and (−10,0).
2. Consider the line integral I C F · d r, where the vector field F...
2. Consider the line integral I C F · d r, where the vector field F = x(cos(x 2 ) + y)i + 2y 3 (e y sin3 y + x 3/2 )j and C is the closed curve in the first quadrant consisting of the curve y = 1 − x 3 and the coordinate axes x = 0 and y = 0, taken anticlockwise. (a) Use Green’s theorem to express the line integral in terms of a double...
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.
1.) Let f(x,y) =x^2+y^3+sin(x^2+y^3). Determine the line integral of f(x,y) with respect to arc length over...
1.) Let f(x,y) =x^2+y^3+sin(x^2+y^3). Determine the line integral of f(x,y) with respect to arc length over the unit circle centered at the origin (0, 0). 2.) Let f ( x,y)=x^3+y+cos( x )+e^(x − y). Determine the line integral of f(x,y) with respect to arc length over the line segment from (-1, 0) to (1, -2)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT