Please help solve the following question with steps. Thank you!
6. Compute JF . T ds where F (-y,z) and (a) C is the line segment from (1,0) to (0,0) followed by...
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (iv) 2π, with a a positive constant. t for C the curve (cost +tsint,sint tcost, 0) for Osts v3 (Hint for (i): use the parametrization (z, y, z) = (t, 1-t, 0) for 0 1) t (1)...
5. Compute the line integral ſc fds, where a) C is the line segment from (3,4,0) to (1,4, 2) and f(x, y, z) = x + y2. b) C is the curve y = x2 from (0,0) to (3,9) and f(x,y) = 3x. c) C is the upper half of the circle of radius 2 from (2,0) to (-2,0) and f(x,y) = y.
(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...
X 16.1.19 Evaluate Sxas x ds, where C is С t a. the straight line segment x =t, y= 5, from (0,0) to (20,4) b. the parabolic curve x =t, y = 262, from (0,0) to (1,2)
Sc 3x?yz ds, where C: x=t, y =ť, z = {1,0 <t<l.
(b) Evaluatex + 2y ds where C is the portion of quarter-circle centered at the origin with the clockwise rotation from (-3,0) to (0,3) which in turn is followed by the line segment from 0,3) to (6,2). (10 marks) (c) Let F = (2x2y, ya), a closed curve C and let D be the region enclosed by the curve. The region R is in the first quadrant bounded by the r-axis, the line x = 1 and the curve y...
A B C Parametrize, but do not evaluate, //f(x, y, z) ds, where f(x, y, z) 2y22 and S is the part , where J(,y,) 3 3 and 0 Sys4 of the graph of z2 over the rectangle -2 s . Parametrize, but do not evaluate, F.n ds, where F (,-,z) and S is the sphere of radius 2 centered at the origin. Calculate JJs xyz dS where S is the part of the cone parametrized by r(u, u) (ucos...
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....
please be clear as possible. thanks 2. Evaluate the line integral where C is the given curve: BE SURE THAT YOU PARAMETERIZE EACH CURVE! (a) e dr where C is the are of the curve r y' from (-1,-1) to (1, 1): (b) dr dy where C conusists of the arc of the circle 2+ 4 from (2.0) to (0.2) followed by the line segment from (0.2) to (4,3) (c) y': ds where C is the line segment from (3,...
Evaluate where C is the boundary of the graphs of from (0,0) to (2,8) followed by a straight line segment from (2,8) to (0,0). We were unable to transcribe this imagey = 21