1. [-/1 Points] DETAILS LARCALC11 15.3.006. Need Help? Read it With MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following vector field F(x, y) = Mi + Nj F(x, y) = yi + x) 5. [-/1 Points] DETAILS LARCALC11 15.3.027. (a) Show that F is conservative. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate F . or along each path. (Hint: If F is conservative, the integration may be easier on an alternative path.) (b) Verify that the value of F . or is the same for each parametric representation of C. F(x, y. z) - yal + xxj + xyk (a) Car,(t) = 1+ 3) +th, Osts9 () C: r, (1) = (4 +131+ (5 - mosts F . de - (b) (2:ry(1) =1 +4+ck, osts3 (11) C2: (2(w) = (4 + In(wiji + (5 - In(will. iswse Need Help? Read Watch it Need Help? Read it 6. [-/1 Points] DETAILS LARCALC11 15.3.032. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 2. [-/1 Points] DETAILS LARCALC11 15.3.010.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate F . or along each path. (Hint: If F is conservative, the integration may be easier on an alternative path.) F(x, y, z) = y sin(2)i + x sin(z)j + xy cos(x]k Evaluate F . dir using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. (a) C:r,() =1 +ry. osts4 (16(8x + 5y)1 + 10(8x + 5y)1] . or Ci smooth curve from (-5, 8) to (3, 2) (b) C2: Fy(() = 1601 + 160, Ost s 1 Need Help? Read My Watch ! Master Need Help? Read it 3. [-/1 Points] DETAILS LARCALC11 15.3.015. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate /F . or using the Fundamental Theorem of Line Integrals. Use a computer algebra system erify your results. (Sz + 5y) edx + (5x - 2x) dy + (5x - 2y) de () Ci 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 Watch