8 points each 1. F is a conservative vector field. Evaluate ScF. dr where F =<...
Let F(XYZ) = <2y27, 4xyz, 2xy2> be a vector field. (a) Knowing that F is conservative, find a function f such that F = vfand f(1,2,1) = 8. (b) Using the result of part(a), evaluate the line integral of F along the following curve C from (0,0,0) to (3.9, 1.8, 2.3). y2 + x4z2 + 2x4(x3 + y2 + 24)1/2 = K Kis a constant .- Answer:
Let F(x,y,z) = <2y2z, 4xyz, 2xy2> be a vector field. (a) Knowing that F is conservative, find a function f such that F = Vf and f(1,2,1)= 8. (b) Using the result of part(a), evaluate the line integral of F along the following curve C from (0, 0, 0) to (3.9, 1.4, 2.6). y2 + x4z3 + 2xy(x3 + y4 + 24)1/3 = K ; K is a constant Answer: Next page
4. Use the Fundamental Theorem for Conservative Vector Fields to compute F. dr. where F= <3y2 - 4x3y3,6xy - 3x*y2 > and C is parametrized by r(t) = < e. +9 > from t = 0 to 1= 2.
F. dr Find a function of such that of 8 and then evaluate where F(x, y) = < 3 + 2kg", 2y) and C is any smooth curve from (-2, 1) to (1,2).
7. Is F(x, y) =< 2x, 6y? > a conservative vector field?
Consider the vector field F (x, y, z) = <y?, z2, x?>. Compute the curl (F). Use Stokes' Theorem to evaluate S. F. dr where C is the triangle (0,0,0), (1,0,0), and (0, 1, 1) oriented counter-clockwise when viewed from above.
Calculate the work done by the vector field F(x,y)=4xy, 2x2 along a smooth, simple curve from point (3, −1) to point (4, 2) We were unable to transcribe this imageWe were unable to transcribe this image
Let F =< eycos(x) + 5y + 1, eysi x) + 8x > be a vector field in R2. Use Green's Theorem to evaluate F. dr where C is the curve oriented counter-clockwise and composed of the arc of the curve y=x2 – 4 starting at (-1, -3) and ending at (1, -3). and followed by the line segment going from (1, -3) to (-1, -3)
I lost in this I need help please thank you 5) [8] Evaluate ds , where C is the curve y=-x4 1<x<2. 7 X
1. One of the two vector fields listed below is conservative. The other one is not conservative. (a) Determine which one of these fields is conservative. Label the conservative field F and and find a potential function f for it. Label the other field G and prove that G is NOT conservative. (b) Use the fundamental theorem of line integrals to compute SCF . dr, where C is the curve parameterized by (c) Compute Jc G-dr, where C is the...