Gmail YouTube Maps Assignment Scoring Your last submission is used for your score. 1. [-/1 Points] DETAILS LARCALC11 15.3.006. Consider the following vector field F(x, y) = Mi + Nj. F(X, y) = yi + xj (a) Show that F is conservative. aN aM ax ay (b) Verify that the value of F . dr is the same for each parametric representation of C. C (i) cq : r (t) = (3 + t)i + (4 - t)j, ost= 1 F . dr = ( ii) C2: 5 2 ( W) = (3 + In(w))i + (4 - In(w))j, is wse F . dr = Need Help? Read It 1 85OF Smoke Q SearchSubmit Answer 2. [-/1 Points] DETAILS LARCALC11 15.3.013. Evaluate F . dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. ex sin (y) dx + ex cos( y) dy C: cycloid x = 0 - sin(0), y = 1 - cos(0) from (0, 0) to (2nt, 0) Need Help? Read It Watch It Submit Answer 3. [-/1 Points] DETAILS LARCALC11 15.3.015. Evaluate F . dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. ( 52 + 3y ) dx + ( 3x - 32 ) dy + ( 5x - 3y)'dz (a) C: line segment from (0, 0, 0) to (1, 1, 1) (b) C: line segment from (0, 0, 0) to (0, 0, 1) to (1, 1, 1) (c) C: line segment from (0, 0, 0) to (1, 0, 0) to (1, 1, 0) to (1, 1, 1) Need Help? Read It Watch It Submit Answer.Submit Answer 4. [-/1 Points] DETAILS LARCALC11 15.3.027. Evaluate F . dr along each path. (Hint: If F is conservative, the integration may be easier on an alternative path.) F (x, y, z ) = yzi + xzj + xyk (a) C1: 1, (t ) = ti + 2j + tk, osts4 ( b ) C 2 : 5 2 ( t ) = 12i + tj + + 2 k, Osts 2 Need Help? Read It Watch It Submit Answer 5. [-/1 Points] DETAILS LARCALC11 15.3.032. Evaluate F . dr along each path. (Hint: If F is conservative, the integration may be easier on an alternative path.) F ( x, y, z) = y sin(z) i + x sin(z)j + xy cos(x)k (a) C1: 1, (t ) = 12i + 12j, ost= 4 (b ) C2: 12 (t ) = 16ti + 16tj, Ost