(4,9,-5) Evaluate the integral | ydx+x dy +7 dz by finding parametric equations for the line...
(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)
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.
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3) 5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
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....
Evaluate the line integral | * dr + 2diu + g? ds. 22 dx + x? dy + y2 dz, where C is the line segment from (1,0,0) to (4,1,2).
Problem 18. 7/2 (1 point) Evaluate the iterated integral AIT cos(x+y+z) dz dx dy. Answer:
please calculate directly, my answer is (3/2)pi+32/3 is that correct? (15%) Evaluate the line integral -r-y + ) dz+ (z+2cy+3)dy, where C consists of the arc Ci of the quarter circle +y 1,x 2 0,y 0, from (0,-1) to (1,0) followed by the arc C2 of the quarter ellipse 4z2y2 - 4, 2 0, y 20, from (1,0) to (0, 2) (15%) Evaluate the line integral -r-y + ) dz+ (z+2cy+3)dy, where C consists of the arc Ci of the...
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)
Evaluate the line integral. fr de x² dx + y²dy, where C is the arc of the circle x2 + y2 = 4 from (2,0) to (0,2) followed by the line segment from (0, 2) to (4,3).
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise. 12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.