Evaluate the line integral. My answer comes out to be 0 meaning F is conservative. Is there any o...
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....
(5,3,-2) Evaluate the integral y dx + x dy + 4 dz by finding parametric equations for the line segment from (2,1,5) to (5,3,-2) and evaluating the line integral of (2,1,5) F = yi + x3 + 4k along the segment. Since F is conservative, the integral is independent of the path. (5,3,-2) y dx + x dy + 4 dz= (2,1,5)
Evaluate line integral ( F. dr where C is any positively oriented simple closed curve that encloses the origin by using a circle of radius r, and r is small enough so that the circle lies entirely inside C given F(x, y) = ? 1)_ 2xyi +(y2 – xº)j Ans (x² + y²)
Show that the line integral is independent of path by finding a function f such that ∇f = F. C 2xe−ydx + (2y − x2e−y)dy, C is any path from (1, 0) to (4, 1) f(x, y) = Evaluate the integral.
Recall that it is conservative, then the line intera/ F.dr is path-independent meaning that the the integral depends only on the initial and terminal bolets of the sath, and not on the path Similar ideas are true for surfaces, although we must now discuss the curl instead of the gradient. Note that there is some vector field A such that (V x A) = F. then Suo ' Theorem tells us that JP as - x A). S = 6...
(6) Show that F(x, y) = (x+y)i + (**)is conservative. (a) Then find such that S = F (potential function). (5) Use the results in part(a) to cakulae ( F. ds along C which the curve y = a* from (0,0) to (2,16). (2) Use Green's Theorem to evaluate 1. F. ds. F(1,y) =(yº+sin(26))i + (2xy2 + cos y)and C is the unit circle oriented counter clockwise (6) Evaluate the surface integral || 9. ds. F(x,y,z) = xi +++where S...
3. (12 points) Evaluate the line integral S y3dx + (x3 + 3xy2)dy , where C is the path from (0,0) to (1,1) along the graph y = x3 and from (1,1) to (0,0) along the graph of y=x.
there is first question E then there is the question
of the value of the line integral ,then quwstion A, then question
1, and the last two pictures are one question
Question E (5 points) By Green's theorem, the value of the line integral y 4 is: , where C is the curve given by a) 3 c) 12t d) 27T e) If none of the above is correct, write your answer here in a box rover the line segment...
QUESTION 10 (a) Verify that the force field F = yi+zj+4k s conservative. By finding its potential function ф, evaluate the work done by F in moving a particle over the path from (6 marks) Apply Green's Theorem to evaluate the line integral фу2dr+x2dv in which C is (b) the boundary of a triangle made by x-0, x+y-1, y-0 (6 marks)