Question

Let C be the circle with radius 1 and with center (−2,1), and let f(x,y) be...

Let C be the circle with radius 1 and with center (−2,1), and let f(x,y) be the square of the distance from the point (x,y) to the origin.

Evaluate the integral ∫f(x,y)ds

Homework Answers

Answer #1

if satisfied with the explanation, please rate it up..

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
Let (X,Y) be chosen uniformly from inside the circle of radius one centered at the origin....
Let (X,Y) be chosen uniformly from inside the circle of radius one centered at the origin. Let R denote the distance of the chosen point from the origin. Determine the density of R. From there, determine the density of the random variable R2 = X2 + Y2.
Problem 10. Let F = <y, z − x, 0> and let S be the surface...
Problem 10. Let F = <y, z − x, 0> and let S be the surface z = 4 − x^2 − y^2 for z ≥ 0, oriented by outward-pointing normal vectors. a. Calculate curl(F). b. Calculate Z Z S curl(F) · dS directly, i.e., evaluate it as a surface integral. c. Calculate Z Z S curl(F) · dS using Stokes’ Theorem, i.e., evaluate instead the line integral I ∂S F · ds.
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)
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?
7. F(x,y)=3xy, C is the portion of y=x^2 from (0,0) to (2,4) evaluate the line intergral...
7. F(x,y)=3xy, C is the portion of y=x^2 from (0,0) to (2,4) evaluate the line intergral (integral c f ds)
. Let C be the curve x2+y2=1 lying in the plane z = 1. Let ?=(?−?)?̂+??...
. Let C be the curve x2+y2=1 lying in the plane z = 1. Let ?=(?−?)?̂+?? = (a) Calculate ∇×? (b) Calculate ∫?∙?? F · ds using a parametrization of C and a chosen orientation for C. (c) Write C = ∂S for a suitably chosen surface S and, applying Stokes’ theorem, verify your answer in (b) (d) Consider the sphere with radius √22 and center the origin. Let S’ be the part of the sphere that is above the...
Consider the vector field below: F ⃗=〈2xy+y^2,x^2+2xy〉 Let C be the circular arc of radius 1...
Consider the vector field below: F ⃗=〈2xy+y^2,x^2+2xy〉 Let C be the circular arc of radius 1 starting at (1,0), oriented counter clock wise, and ending at another point on the circle. Determine the ending point so that the work done by F ⃗ in moving an object along C is 1/2.
Evaluate ∫c(1−xy/2)dS where C is the upper half of the circle centered at the origin with...
Evaluate ∫c(1−xy/2)dS where C is the upper half of the circle centered at the origin with radius 1 with the clockwise rotation followed by the line segment from (1,0)to (3,0) which in turn is followed by the lower half of the circle centerd at the origin of radius 3 with clockwise rotation.
A particle of mass m moves about a circle of radius R from the origin center,...
A particle of mass m moves about a circle of radius R from the origin center, under the action of an attractive force from the coordinate point P (–R, 0) and inversely proportional to the square of the distance. Determine the work carried out by said force when the point is transferred from A (R, 0) to B (0, R).
Consider the hemispherical shell of inner radius 3 and outer radius 7. The mass density at...
Consider the hemispherical shell of inner radius 3 and outer radius 7. The mass density at any point P(x,y,z) is directly proportional to the square of the distance from P to the origin. Set up an integral in an appropriate coordinate system for the moment of inertia about the z-axis. Simplify your integrand as much as possible, but do not evaluate the integral.